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

git clone: git://git.pablopie.xyz/lie-algebras-and-their-representations
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Commit: d03eee11d00a802c7101493830dd6145e6823355
Parent: 0c9359752bfc2d4f88353db8b8b68c23e355fbdc
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 16 Nov 2022 22:32:54 +0000

Clarified a comment on Lie algebra cohomology

Diffstat

1 file changed, 3 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/semisimple-algebras.tex	5	3	2

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -623,8 +623,9 @@ non-trivial finite-dimensional irreducible \(V\), \(i > 0\). For \(K =
 \mathbb{C}\), the Lie algebra cohomology groups of an algebra \(\mathfrak{g} =
 \mathbb{C} \otimes \operatorname{Lie}(G)\) are intimately related with the
 topological cohomologies -- i.e. singular cohomology, de Rham cohomology, etc.
--- of \(G\). We refer the reader to \cite{cohomologies-lie} and
-\cite[sec.~24]{symplectic-physics} for further details.
+-- of \(G\) with coefficients in \(\mathbb{C}\). We refer the reader to
+\cite{cohomologies-lie} and \cite[sec.~24]{symplectic-physics} for further
+details.
 
 Complete reducibility can be generalized for arbitrary -- not necessarily
 semisimple -- \(\mathfrak{g}\), to a certain extent, by considering the exact