- Commit
- d2c1e21e268cd01331407b312ab6f851c8340753
- Parent
- a5d65523bcef5b92d8d8e3ec318bda933197a855
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Fixed a TODO item
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Fixed a TODO item
1 file changed, 1 insertion, 2 deletions
Status | File Name | N° Changes | Insertions | Deletions |
Modified | sections/complete-reducibility.tex | 3 | 1 | 2 |
diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex @@ -1,6 +1,5 @@ \chapter{Semisimplicity \& Complete Reducibility} -% TODO: Update the 40 pages thing when we're done Having hopefully established in the previous chapter that Lie algebras and their representations are indeed useful, we are now faced with the Herculean task of trying to understand them. We have seen that representations are a @@ -8,7 +7,7 @@ remarkably effective way to derive information about groups -- and therefore algebras -- but the question remains: how to we go about classifying the representations of a given Lie algebra? This is a question that have sparked an entire field of research, and we cannot hope to provide a comprehensive answer -the 40 pages we have left. Nevertheless, we can work on particular cases. +the 47 pages we have left. Nevertheless, we can work on particular cases. For instance, one can redily check that a representation \(V\) of the \(n\)-dimensional Abelian Lie algebra \(K^n\) is nothing more than a choice of