lie-algebras-and-their-representations

Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules

fd788d60 — Pablo

Updated a link in README.md

4b0f01e4 — Pablo

Updated the references to my academic website

60b52003 — Pablo

Updated the README

e1e36e39 — Pablo

Changed the document title

045bad58 — Pablo

Added an "under construction" note to the preface

2738a681 — Pablo

Broke up a paragraph in the acknowledgments

e6d7a5f1 — Pablo

Added a link to a copy of the CC4 license

164cd5a2 — Pablo

Restructured the preface

cada79b6 — Pablo

Minor tweak in language

1ff66bd2 — Pablo

Added some TODO items

f5e1d9a7 — Pablo

Minor tweak in notation

1b8026a4 — Pablo

Started to work on hydrating the final chapter

212b52e1 — Pablo

Fixed some typos

fc393aa5 — Pablo

Added a TODO item

9e9211b9 — Pablo

Added a proof

7b33177a — Pablo

Added a proof

4c910651 — Pablo

Minor tweak

0e094c94 — Pablo

Added some comments on the graph structure of 𝓑

c45df8a9 — Pablo

Added some comments on the proof of a proposition

e644c3d0 — Pablo

Added the classification of coherent sl(2)-families as an example

aa77f553 — Pablo

Demoted a proposition to a lemma

88fc2197 — Pablo

Revised some TODO items

68397c8a — Pablo

Minor tweak to the statement of a lemma

c7ee9fa8 — Pablo

Fixed a typo

81613876 — Pablo

Added a joke 😛

9fbf6530 — Pablo

Fixed a calculation error

514cc87c — Pablo

Tweaked the statement of a theorem

c7ec3b45 — Pablo

Changed the spacing of the diagrams on the connected components of 𝓑

da5c06bd — Pablo

Added some proofs to the last chapter

9b7c99d6 — Pablo

Fixed multiple issues in the discussion of the graph 𝓑

17698441 — Pablo

Added the statement of a lemma

930a094e — Pablo

Demoted a proposition to a lemma

d9336d2c — Pablo

Changed the notation for the set of parameters for coherent families

f02b089f — Pablo

Added further details to a theorem

d7bc482e — Pablo

Added a definition

246a9562 — Pablo

Added sp(2n) to the list of simple Lie algebras

df1d4f69 — Pablo

Revised the comments on regular and integral sl(n)-sequences

08ae3830 — Pablo

Standardized the notation for the dot action

871dcf70 — Pablo

Added further results on Weyl groups

5ca736e5 — Pablo

Fixed two typos

d34e8ad6 — Pablo

Minor tweak in notation

c2a9394c — Pablo

Changed the notation of the last chapter

7116b6fb — Pablo

Changed the notation for the graph 𝓟

a59903dd — Pablo

Removed a TODO item

52ddd24e — Pablo

Added a TODO item

411aa9df — Pablo

Changed the notation for the elements of the defining basis of Δ for sl(3)

47cef582 — Pablo

Elaborated on a TODO item

7fc1115c — Pablo

Fixed a typo

b9d6e063 — Pablo

Added a skeleton for the chapter on coherent families

4de50acb — Pablo

Elaborated on the definition of the symplectic Lie algebras

98d779d6 — Pablo

Properly finished off the chapter on simple weight modules

5545975b — Pablo

Added a file for the chapter on the classification of coherent families

529c42b1 — Pablo

Fixed a typo

578ea36b — Pablo

Minor tweak in notation

63e0e13f — Pablo

Added a "last updated" notice to the licesing information

f6f0a68a — Pablo

Minor tweaks to the intro to the section on Verma modules

2a9196f3 — Pablo

Tweaker the text in the preface

09fea928 — Pablo

Minor tweak in notation

20117e2e — Pablo

Fixed a small typo

6b756236 — Pablo

Fixed a typo

4486d7c0 — Pablo

Revised the discussion on Fernando's work

3e2e4508 — Pablo

Corrected the remarks on Verma modules of antidominant weights

437ed300 — Pablo

Corrected the definition of the order in the root lattice

88d8fe84 — Pablo

Restructured the section on Verma modules

0e9e90d3 — Pablo

Fixed a typo

6b76e44e — Pablo

Removed duplicate labels

9bbab87c — Pablo

Renamed some files

7abeda5b — Pablo

Tweaked some notation

96d61615 — Pablo

Fixed another typo

318630c4 — Pablo

Fixed a typo

5c42a67d — Pablo

Turned a footnote into a regular sentence

e00ce51f — Pablo

Simplified an example

0d471bdc — Pablo

Corrected the last chapter

2b0f9998 — Pablo

Removed the catalographic card from the notes

5158fbe3 — Pablo

Minor tweak in notation

5c69cc58 — Pablo

Changed the notation for the PBW Theorem

3eebca52 — Pablo

Added further comments on simple modules of the direct sum

896a555b — Pablo

Simplified the code for boxed theorems

eb986e43 — Pablo

Added a proof of a proposition

c389afd8 — Pablo

Cleaned the code for boxed theorem environments

0025360c — Pablo

Removed manual page breaks

3ec5b4c1 — Pablo

Further refined the styles of boxed theorem environments

29d396ad — Pablo

Made it so that enumerate items are colored

7ead97da — Pablo

Refined the style of the theorems

09f25352 — Pablo

First draft of an implementation of colored/boxed theorem environments

3e0363aa — Pablo

Replaced the term "admissible" with the term "bounded"

91433815 — Pablo

Reoriented communative diagrams to avoid arrows going up

cac93e79 — Pablo

Fixed a typo

f309228f — Pablo

Clarified a sentence

f8134e9f — Pablo

Added a clarification to the discussion on cohomology

9369503b — Pablo

Added a clarification to the discussion on cohomology

647da297 — Pablo

Fixed the name of the standard resolution of the trivial module

41970a21 — Pablo

Fixed a typo

26deb194 — Pablo

Replaced a reference

f5176707 — Pablo

Fixed a major error on cohomology

6deab873 — Pablo

Clarified the analysis of 𝔰𝔩₂

cdfa28f3 — Pablo

Minor improvement in the notation of a proof

5b7bf9c8 — Pablo

Fixed a minor typo

65e93388 — Pablo

Added some qualifiers to the statement about the Lie functor for algebraic groups

c3773211 — Pablo

Minor improvement in notation

91c6c49f — Pablo

Minor tweak in language

032c0da6 — Pablo

Fixed a few typos

b76b7ac3 — Pablo

Minor tweak to an equation

568276a6 — Pablo

Corrected errors in a reference

255321a7 — Pablo

Added further comments to the section on cohomology

e7eac0dc — Pablo

Added funther comments on algebraic groups

d16a340f — Pablo

Minor tweak in notation

7e9e9bc4 — Pablo

Cleaned the section on Verma modules

87ce54ef — Pablo

Removed the TODO list

88accd95 — Pablo

Tweaked some sentences

19a49a96 — Pablo

Added further comments on the proof of the Highest Weight Theorem

36867274 — Pablo

Fixed a comment on the monoidal structure of g-Mod

3acac392 — Pablo

Repharased a sentence

fc675b6a — Pablo

Added further details to a theorem

f4df5a41 — Pablo

Fixed a typo

f2b649f6 — Pablo

Added further details to a remark

d1d46359 — Pablo

Changed the notation for the Casimir element

b9cb12e4 — Pablo

Added some further comments on the Chevalley-Eilenberg resolution

d9a5b64b — Pablo

Changed the notation for the Killing form

3c1c2058 — Pablo

Updated the TODO list

af06ac4d — Pablo

Changed the notation for twisted modules (yet again)

b9179fc8 — Pablo

Minor correction to the introduction

43d2de9e — Pablo

Fixed some typos

2f81acdf — Pablo

Extracted a result to a couple of examples

76753d1d — Pablo

Credited Weyl in a proof

9900613a — Pablo

Changed the notation for differential operators

1ff40e69 — Pablo

Fixed a typo

41f85501 — Pablo

Demoted a theorem to a proposition

d0cbf9ca — Pablo

Fixed a typo

0904c078 — Pablo

Fixed some typos

3ba5201f — Pablo

Changed the notation for twisted modules

aebf9810 — Pablo

Added some further clarification on what we assume

382c22ef — Pablo

Fixed a typo

c3b67b1a — Pablo

Added an index to the document

2bb1792f — Pablo

Updated the .gitignore

cefadc8b — Pablo

Cleaned the code for commutative diagrams

3130aacc — Pablo

Added a catalographic card and a title page

d00a617f — Pablo

Added a TODO list

ddfe92ba — Pablo

Fixed some typos

b33d5814 — Pablo

Switched the notation for a dominat weight in chapter 1

41a980cb — Pablo

Added further clarifications on invariants

09bbf643 — Pablo

Fixed some typos

1d71b805 — Pablo

Switched the notation for completely reducible moddules

d06a7808 — Pablo

Fixed a typo

ec9370a1 — Pablo

Fine-tuned the notation for Methieu's coherent extension

d1b26631 — Pablo

Changed the notation for the Weyl group

491346ac — Pablo

Fixed some typos

04151543 — Pablo

Switched the notation for a dominat weight in chapter 5

aa6634bc — Pablo

Switched the notation for a dominat weight in chapter 4

594ddfee — Pablo

Reworked the introduction of the 3rd chapter

0becfef5 — Pablo

Merge branch 'master' into module-notation

40f3ff33 — Pablo

Changed the title of chapter 3

6caa44df — Pablo

Switched the notation for a dominat weight in chapter 3

2cb4d099 — Pablo

Switched the notation for modules/representations in the third chapter

5d7960d5 — Pablo

Switched the notation for modules/representations in the second chapter

6b122954 — Pablo

Added a clarification

3a4bb936 — Pablo

Changed the notation for Mathieu's coherent extension

e20b0db3 — Pablo

Fixed the reference to Kirillov

07c9030a — Pablo

Fixed some typos

b9b5ca88 — Pablo

Fixed a major error in the proof of complete reducibility

277e277c — Pablo

Minor tweak in the references

c0974a02 — Pablo

Clarified the ortogonality relations in the weight diagrams of sl3

491b2cba — Pablo

Repharased a sentence

59f4eea9 — Pablo

Added a reference to the concept of adjoint functors

b10f1352 — Pablo

Added clarifications on the functoriality of a construction

ec419041 — Pablo

Minor tweak in language

e968ddeb — Pablo

Added a reference to the non-fullyness of the Lie functor for algebraic groups

3f990683 — Pablo

Renumbered theorems and definitions

a9e93614 — Pablo

Fixed some typos

b3c896fe — Pablo

Repharased a sentence

4036d481 — Pablo

Changed a single word

65d40132 — Pablo

Fixed some typos

214d065f — Pablo

Repharased a sentence

2b4ab7e6 — Pablo

Fixed some typos

3c9f6c61 — Pablo

Removed a reference to the title of a book

45e040d1 — Pablo

Clarified the PBW theorem

841a1a48 — Pablo

Fixed a typo

6b00f279 — Pablo

Added the definition of the dimension of a Lie algebra

d0aecccb — Pablo

Fixed multiple typos

8e31e9df — Pablo

Capitalized named theorems and definitions

5cd9ad99 — Pablo

Sorted the bibliography

3e623513 — Pablo

Removed abreviations

bec199c9 — Pablo

Changed the notation in an example

c3789a20 — Pablo

Fixed a typo

a9a2e0c9 — Pablo

Merge branch 'master' into font-change

33067d0d — Pablo

Changed the notation for the Jordan decomposition

f1f671e0 — Pablo

Merge branch 'master' into font-change

6cdd06ed — Pablo

Changed the styling of a weight diagram

f8278777 — Pablo

Merge branch 'master' into font-change

50666a02 — Pablo

Added a link to the compiled document in the README

1e697b86 — Pablo

Merge branch 'master' into font-change

5c6eacf8 — Pablo

Simplfied a URL

7e421093 — Pablo

Changed the color of links

34fac7fd — Pablo

Replaced the monospace font for the TXTT font

92005a04 — Pablo

Fixed a typo

d721e2b5 — Pablo

Replaced the standard LaTeX font with the Palladio font family

7e30d20a — Pablo

Changed the notation for the localization of a ring

b1fd8dc0 — Pablo

Minor tweak in notation

498abf26 — Pablo

Minor tweak in language

271ee360 — Pablo

Minor tweak in notation

52da5747 — Pablo

Fixed a typo in the references

a2de1ebb — Pablo

Added some further thanking

ba25b90a — Pablo

Fixed a typo

41a8f18b — Pablo

Added a minor clarification

134990e9 — Pablo

Added a drawing to the section on sl2

2a648647 — Pablo

Fixed multiple typos

31a0cde2 — Pablo

Made it so that the pages beforen the start of the first chapter are not numbered

a79b5742 — Pablo

Added a blank page after the dedication

9a9e418f — Pablo

Fixed multiple typos

08624249 — Pablo

Fixed typos

b4d5b068 — Pablo

Made the "1" in "1-dimensional" upwrite

dd64c565 — Pablo

Revised the forth chapter

9254cd72 — Pablo

Revised the third chapter for a third time!

f6e2ffa6 — Pablo

Minor clarification

4adde1a1 — Pablo

Fixed a definition

359ba13b — Pablo

Cleaned the references

325ddfd3 — Pablo

Clarified some notation

6bf62206 — Pablo

Simplified the preamble

44e2669c — Pablo

Removed a redefinition of a macro

238d43d0 — Pablo

Fixed a typo

4f800549 — Pablo

Removed the macros for double-struck letters

873e879e — Pablo

Incorporated hidden statements into the statement of a theorem

578d7a44 — Pablo

Added a proof of a technical result

12047085 — Pablo

Removed duplicate words

7c14f2cb — Pablo

Fixed some typos

45e2a2f1 — Pablo

Fixed a typo

ec2335c5 — Pablo

Fixed multiple typos

5e6751ba — Pablo

Removed Lucas full name

75220017 — Pablo

Revised the final chapter

121602d7 — Pablo

Revised the forth chapter

bf3eff97 — Pablo

Clarified the action of g in V*

a20afde8 — Pablo

Added some remarks

82c5321e — Pablo

Replaced the word "killed" by "annihilated"

124b15e9 — Pablo

Revised the third chapter (again)

7ec8aac7 — Pablo

Fixed a major typo

9788260f — Pablo

Revised the second chapter (again)

6002e169 — Pablo

Revised the first chapter (again)

62ebb321 — Pablo

Revised the third chapter

e2decc85 — Pablo

Fixed a typo

6b87d446 — Pablo

Added notes on how coherent families are useful in other problems

e7bf45af — Pablo

Automated the "47 pages left" thing from chapter 2

e4156ebd — Pablo

Revised the second chapter

984fec64 — Pablo

Standardized the word "one-dimensional"/"1-dimensional"

8a163c17 — Pablo

Standardized the word "nonzero"/"non-zero"

44628b7f — Pablo

Revised the first chapter

86586de2 — Pablo

Fixed multiple typos

9758560c — Pablo

Minor styling tweak

4f991107 — Pablo

Fixed the alignment of the title in the cover

d4aff46c — Pablo

Clarified some notation

4cc54e0b — Pablo

Rewrote the preface

0cde29f0 — Pablo

Changed the title of the introduction

02ff7321 — Pablo

Fixed a TODO item

d2c1e21e — Pablo

Fixed a TODO item

a5d65523 — Pablo

Completed the notes with a catchphrase

ed5d850d — Pablo

Added a small conclusion to the introduction

83065bba — Pablo

Added some remarks

33044eaf — Pablo

Removed a TODO item

5dbf8e99 — Pablo

Added the direct sum of Lie algebras to the list of examples

fe6b8b35 — Pablo

Added the box product of representations to the list of examples

ac576ee0 — Pablo

Reworked some of the discussion on representations

5de2403f — Pablo

Added a conclusion to the chapter on Mathieu's work

2ed2d069 — Pablo

Added the definition of the subrepresentation generated by an element

596ee686 — Pablo

Added a small clarification in a proof

16983579 — Pablo

Added a TODO item

188e843d — Pablo

Added notes on the "uniqueness" part of the highest weight theorem

d88a4932 — Pablo

Promoted some TODO items

53685018 — Pablo

Added notes on the intuition behind a proof

5d0dff68 — Pablo

Tied up transitions between sections in chapter 4

c30d5168 — Pablo

Fixed an error

9023cb60 — Pablo

Fixed some typos and added a clarification

baf42975 — Pablo

Changed the notation for the height of a weight

97ef29fc — Pablo

Fixed a typo

bbda34fd — Pablo

Reworked the subdivision of the forth chapter

e066394b — Pablo

Fixed a sign in some equations

f72a9a6c — Pablo

Added a TODO item

3fa78459 — Pablo

Defined the action of the Weyl group in g

e50e8bf3 — Pablo

Changed the notation for elements of the Weyl group

3e715aa9 — Pablo

Removed TODO items

5bed83af — Pablo

Added a TODO item

f7480a43 — Pablo

Reordered the contents of the chapter on the general finite-dimensional setting

85ee514a — Pablo

Added TODO items

58d706bd — Pablo

Rewrote the introduction of the chapter on sl2 and sl3

369f54cb — Pablo

Changed the names of some sections

e5c68abc — Pablo

Reordered the contents of the section on sl3

36b566c9 — Pablo

Minor improvement in the notation of a proof

e2ec70dd — Pablo

Added TODO items

11242f80 — Pablo

Fixed the proof on the theorem on D-modules

273cce63 — Pablo

Removed unnecessary comment

4487ff47 — Pablo

Modified the proof of the dominant integral weight theorem for sl2

32a36d3f — Pablo

Reordered some equations

394316a2 — Pablo

Incorporated the section on sl3 in the introduction of the chapter on sl3

854e67bc — Pablo

Removed a stupid epigraph

9c254f28 — Pablo

Fixed a typo

a4e3dcf2 — Pablo

Reordered some equations

fc3472fb — Pablo

Moved the discussion on representations of arbitrary semisimple algebras to a separate chapter

806656c8 — Pablo

Tied up the conclusion of the chapter on complete reducibility

293ed6c5 — Pablo

Cleaned TODO items

7121a171 — Pablo

Added notes on the proof of Cartan's criterium for semisimplicity

d310eab2 — Pablo

Moved the discussion on sl2 and sl3 to a new chapter

490c4786 — Pablo

Started to work on the section on invariant bilinear forms

35b312c7 — Pablo

Incorporated much of the discussion on semisimplicity and complete reducibility to the chapter on sl2

68b7ca86 — Pablo

Renamed a file

283e3378 — Pablo

Renamed the second chapter

3a733453 — Pablo

Added a TODO item

8f196d3f — Pablo

Added the center of a Lie algebra to the list of examples of Abelian algebras

7346488b — Pablo

Added the trivial representation to the list of examples

095e6b71 — Pablo

Removed an example

07e9a939 — Pablo

Fixed multiple typos

bf1dd43e — Pablo

Fixed some typos and clarified some things

706c7496 — Pablo

Added the regular module to the list of examples of representations

37176cc8 — Pablo

Fixed a TODO item

e12c00b7 — Pablo

Cleaned TODO items

f1ad85a0 — Pablo

Added a remark on tensor products

21c5d92c — Pablo

Clarified some notation

c1198935 — Pablo

Added TODO items

aeab267d — Pablo

Hydrated the section on representations

1586220d — Pablo

Reworked a sentence

00010779 — Pablo

Fixed some typos

d8e462db — Pablo

Fixed an example

da7f47c0 — Pablo

Added a TODO item

ac1ac9e8 — Pablo

Added a brief proof of Frobenius reciprocity

197276e1 — Pablo

Updated the TODO list

f96387c5 — Pablo

Hydrated the section the basics of Lie algebras

1ae25bac — Pablo

Reordered the contents of the introduction

f4eec662 — Pablo

Fixed a typo

f9d2b2bc — Pablo

Started to hydrate the introductory chapter

c79c1157 — Pablo

Cleaned the introduction of the second chapter

d03eee11 — Pablo

Clarified a comment on Lie algebra cohomology

0c935975 — Pablo

Edited the example of the Lie algebra of an algebraic group

95cb9df4 — Pablo

Fixed a typo

30591dc4 — Pablo

Fixed a typo

dba06534 — Pablo

Added proofs to some of the theorems of the introduction

ee93c985 — Pablo

Repharased the PBW theorem a bit

346f273a — Pablo

Changed the notation for the algebra of derivations

9608f808 — Pablo

Finished the blueprint of the introduction

01402bde — Pablo

Added the Lie algebra of an algebraic group to the list of examples

e0d774c2 — Pablo

Added the adjoint representation to the list of examples of representations

5c8594f4 — Pablo

Moved the discussion on representations to after the basic results/definitions of Lie algebras

5f645c01 — Pablo

Started to work on the blueprint for the introduction

5926d0c8 — Pablo

Promoved some TODO items

defc4690 — Pablo

Defined the notation for the components of a g-module

65d8e73f — Pablo

Added an adjective

5022a683 — Pablo

Updated the TODO list

fa77efc8 — Pablo

Removed an unnecessary file

f4e5e01e — Pablo

Clarified the meaning of "Zariski topology" in the second chapter

28f2e249 — Pablo

Removed some footnotes

04fa4352 — Pablo

Added references to missing proofs

a761a2d3 — Pablo

Fixed some typos

0e1431c1 — Pablo

Added comments on the lack of functoriality of some of the constructions in the last chapter

19e1433e — Pablo

Added comments on the fact that some automorphisms factor trought some maps

fb51eaf6 — Pablo

Moved the proposition on the multiplicity of irreducible weight modules inside completely reducible weight modules

c20073ce — Pablo

Edited some TODO items

7cda57c5 — Pablo

Hydrated the section on the twisted localization construction

5b5fa385 — Pablo

Removed an unnecessary theorem

51e9c300 — Pablo

Finished hydrating the section on the basics of coherent families and coherent extensions

e439b14d — Pablo

Added an alternative definition of a simple coherent family and some comments on the equivalence between the definitions

1902f952 — Pablo

Changed the notation for irreducible/simple objects in the category of coherent faimlies

b8338a63 — Pablo

Wrote the section on the motivation behind coherent families

0262d38a — Pablo

Added a footnote on the origins of notation

58802aa2 — Pablo

Minor fixes

74854419 — Pablo

Reworked the section on Fernando's work

608942aa — Pablo

Hydrated the section on Fernando's work

f6b00998 — Pablo

Fixed a typo

06cc1a53 — Pablo

Clarified a definition

296df428 — Pablo

Minor tweak in language

ac770d9e — Pablo

Formatted references.bib

4309462a — Pablo

Tied up the example of a representation which is not a weight module

c59b6789 — Pablo

Started to work on hydrating the final chapter

5366d0dd — Pablo

Added a footnote

967dec4c — Pablo

Added a section label

77175706 — Pablo

Removed an unused equivalence from a proposition

015def27 — Pablo

Edited some TODO items

d345d2ae — Pablo

Added the example of the sl2-module on Laurent polynomials

4450a741 — Pablo

Corrected the statement of Fernando's theorem

d89fdc9c — Pablo

Edited some TODO items

d485955b — Pablo

Fixed multiple typos

9955d391 — Pablo

Removed a reduntant formula

ce134141 — Pablo

Minor tweaks

e498f776 — Pablo

Minor correction

23770f04 — Pablo

Finished the proof of a technical lemma

2b67d333 — Pablo

Fixed a typo

00b4ffcd — Pablo

Added a TODO item

9e110cc4 — Pablo

Tweaked the formating of a commutative diagram

391ae2aa — Pablo

Minor tweak

21f35a68 — Pablo

Fixed a typo

391dfe0d — Pablo

Fixed a minor error

0bd82ae0 — Pablo

Mostly finished the proof of Mathieu's classification of which submodules of an irreducible coherent family are cuspidal

41aeb4e4 — Pablo

Updated some TODO items

b84f63fb — Pablo

Changed the notation for the centralizer of the Cartan subalgebra in the universal enveloping algebra

677659b9 — Pablo

Proved the uniqueness of Mathieu's Ext extension

33dbd308 — Pablo

Added TODO items

b0340abf — Pablo

Added a proof the existence of the torsion automorphisms

e9b03cf1 — Pablo

Moved the proof that an admissible module is contained in any of its semisimple coherent extensions to a separate theorem

2e316a8a — Pablo

Formulated the theorem on the semisimplification of a cohenrent family in more abstract terms

271ee342 — Pablo

Replaced the term semisimple for the term completely reducible

7ac14065 — Pablo

Minor corrections

bc27a9d3 — Pablo

Fixed some typos

a0c44092 — Pablo

Removed an unnecessary whitespace

d99a7e17 — Pablo

Fixed a minor error in the definition of a coherent extension

91b949da — Pablo

Added the results we need on Ore's localization

9a4b97f2 — Pablo

Changed the notation for the localization of the modules

3ae1a99d — Pablo

Added a proof of the fact that the localization of an admissible module is well behaved

0431480f — Pablo

Fixed a typo

97047d35 — Pablo

Changed the notation for elements of a basis

c40b5524 — Pablo

Moved the discussion on the existence of a coherent extension to a separate theorem

f9133eab — Pablo

Fixed a typo

a3e69f1f — Pablo

Added a TODO item

61002310 — Pablo

Added references to the discussion on Lie algebra cohomology on "Symplectic techniques in physics"

21b864b6 — Pablo

Changed the notation for the Weyl group

12b23db0 — Pablo

Fixed a typo

463b7079 — Pablo

Incorporated the discussion on how cuspital modules fits inside their extensions to the proof of the existance of Ext

21223791 — Pablo

Changed the notation for the twisting isomorphisms

6456f3ea — Pablo

Started to work on the proof of the existence of Ext

fc7709c4 — Pablo

Added lemmas necessary to prove the existance of Mathieu's Ext extension

43a49d94 — Pablo

Moved the part of the theorem on Ext about the central characters of the irreducible submodules of Ext to a separate theorem

0deb76e3 — Pablo

Moved the theorem on the existence of good coherent extensions to the end of the text

a0a4d291 — Pablo

Added TODO items

1fe5b383 — Pablo

Added a TODO item

a3a506da — Pablo

Fixed a typo

a05908f1 — Pablo

Added further compilation instructions to the README

1d97a3d7 — Pablo

Added TODO items

ecf227a7 — Pablo

Demoted a proposition to the mere status of a lemma

1261dc63 — Pablo

Added minor clarifications

fb5df60b — Pablo

Fixed some typos

5f37c6db — Pablo

Added further clarifications to the proof that V fits nicely inside Ext(V)

07263fd1 — Pablo

Fixed a typo

b51ccc41 — Pablo

Fixed the notation for the composition series in the proof that the semisimplification is a coherent family

b231f997 — Pablo

Fixed the proof that cuspidal modules fit nicely inside their Exts

6b03427a — Pablo

Fixed the definition of the semisimplification of a coherent family

c944e8c3 — Pablo

Added a description of the weight spaces of a subrepresentation of a weight module

0cda2774 — Pablo

Added a proof of the fact that quotients of weight modules are weight modules

41dad6ac — Pablo

Minor change in notation

ca7dc4c8 — Pablo

Removed unnecessary whitespace

650a2716 — Pablo

Added the definition of the semisimplification of a coherent family

09f96046 — Pablo

Added a proof of the fact that any irreducible cuspidal representation is given by M[lambda] for some coherent family lambda

cac9d4ec — Pablo

Fixed a typo

8ef95223 — Pablo

Updated the TODO list

2bfc38f7 — Pablo

Added proper references to the chapter on Mathieu's work to the chapter on semisimple Lie algebras

262948b5 — Pablo

Removed unnecessary whitespace

d4201358 — Pablo

Fixed typos and removed unnecessary whitespace

1fce6426 — Pablo

Completed the proof of complete reducibility

aa6137d8 — Pablo

Completed the proof that every finite-dimensional representation of a semisimple Lie algebra is a weight module

f6e4bb67 — Pablo

Added some items to the TODO list

1dbcc654 — Pablo

Started to work on the chapter about Mathieu's paper

7179f443 — Pablo

Added a TODO list

051116f5 — Pablo

Fixed the comment on the canonical acyclic resolution of the trivial representation

1155a507 — Pablo

Fixed some typos

9b394c58 — Pablo

Added some clarification on language

af132e87 — Pablo

Fixed an error in an equation

16464140 — Pablo

Added an example of Verma module

1fe64a4d — Pablo

Clarified a corolarry on Lie algebra cohomology

6a73599f — Pablo

Properly formated multiline exact sequences

b86fff2d — Pablo

Added information on how to compile the document to the README

1d88b43f — Pablo

Adicionados um README e uma licensa

9a5c23ac — Pablo

Adicionado comentário sobre o fato de que nem todo módulo de dimensão infinita é módulo de peso

65ec951a — Pablo

Revisão ortrográfica

b11c2f71 — Pablo

Terminei de trabalhar na prova do teorema do peso integral dominante

8049a0e0 — Pablo

Corrigido o comentário sobre a prova de redutibilidade completa do Weyl

b4e78e53 — Pablo

Comecei a trabalhar na prova do teorema do peso integral dominante

ee6b5f89 — Pablo

Removidos espalos desnecessários

c4e6ca09 — Pablo

Ajustados comentários iniciais sobre a prova do teorema do peso integral dominante

f21bd352 — Pablo

Ajustados os comentários sobre diagonalização simultânea

f67ace8c — Pablo

Corrigida a prova de que todo módulo de dimensão finita é módulo de peso

9ff3996b — Pablo

Pequena quebra em um parágrafo mais longo

07b9d2a5 — Pablo

Concertados diversos probleminhas ao longo do primeiro capítulo

dab5fa68 — Pablo

Fixed the discussion on the maximal weight

58267a01 — Pablo

Pequenos ajustes gerais no primeiro capítulo

addcf9e5 — Pablo

Concertados mais alguns errinhos gramaticais e frases estranhas

be399204 — Pablo

Concertados varios typos e removidos espaços desnecessários

3c7df239 — Pablo

Terminada (em larga medida) a seção sobre a prova de redutibilidade completa

fcce6df8 — Pablo

Comecei a trabalhar na prova de redutibilidade completa

e8eaf8a1 — Pablo

Concertado o plural no primeirocapítulo

463218b1 — Pablo

Adicionada uma definição mais precisa da subálgebra de Cartan

35df2a44 — Pablo

Ajustado o modelo de numeração dos teoremas

79d7a2ef — Pablo

Corrigidos alguns pecados latéticos

4af135eb — Pablo

Comecei a trabalhar na introdução do capítulo sobre álgebras semisimples

e89ae86e — Pablo

Corrigida a formatação do documento

db1f4163 — Pablo

Alterada a notação para a forma de Killing, de modo a evitar conflitos com a notação do corpo base

98de47f4 — Pablo

Renomeado um arquivo

c120e70f — Pablo

Limpado um pouco do preâmbulo

85424a78 — Pablo

Removidas as dependências nos meus pacotes pessoais

65cbc62f — Pablo

Alterado o estilo da capa

71af4c8d — Pablo

Alterada a notação do corpo base

6bf0af16 — Pablo

Ajustada a dedicatória, o título e o prefácio

e8ad3300 — Pablo

Limpadas mais algumas patologias geometricas e adicionados TODOs

3b9f4057 — Pablo

Limpadas algumas das patologias geometricas das quais padecia esse capítulo

86d679c4 — Pablo

Removidas images no formato PDF do arquivo ZIP do código fonte

1f88875a — Pablo

Adicionadas mais extensões ao .gitignore

cd379670 — Pablo

Commit inicial