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Results tagged with lie-algebra-cohomology
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user 4231
3
votes
Extensions of modules over universal enveloping algebra with fixed central action
The question is indeed somewhat too vague, since a knowledge of certain Ext$^1_\chi$ would be enough to prove the Kazhdan-Lusztig Conjecture: take $M_1$ to be a Verma module and $M_2$ to be a simple h …
- 52.9k
3
votes
What's the most simple proof of Kostant's version of Borel-Weil-Bott for Lie Algebra cohomol...
I'm not sure exactly what your header means, but maybe I can suggest partial answers to your questions. First of all, there are by now many ways to approach the original Borel-Weil theorem, dependin …
- 52.9k
3
votes
Computation of restricted Lie algebra (co)homology
I'm not sure how best to answer the question formulated here, but I can comment further on references. As Dietrich says, there is a large literature. Ever since the foundational work by Jacobson an …
- 52.9k
4
votes
Computing relative Lie algebra cohomology (as appears in Borel-Weil-Bott theorem)
The theorems of Borel-Weil and then Bott, along with Kostant's translation of the ideas into the language of Lie algebra cohomology, do much to illuminate classical representation theory (Cartan-Weyl) …
- 52.9k
7
votes
Whitehead lemmas in Lie algebra cohomology for non-algebraically closed fields
There is no problem about the Whitehead lemmas over an arbitrary field of characteristic 0 in the context of (1) complete reducibility of finite dimensional representations of a semisimple Lie algebr …
- 52.9k
7
votes
Relative Lie Algebra cohomology and sheaf cohomology
As Ben points out, Kostant's papers are a fundamental reference for transition between Bott's work (Annals of Mathematics 66, 1957) involving the flag variety and a more algebraic formulation involvin …
- 52.9k