- Commit
- d03eee11d00a802c7101493830dd6145e6823355
- Parent
- 0c9359752bfc2d4f88353db8b8b68c23e355fbdc
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Clarified a comment on Lie algebra cohomology
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Clarified a comment on Lie algebra cohomology
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