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Results tagged with lie-algebra-cohomology
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user 345
3
votes
Relation between Lie Algebra Cohomology and Number of Relations of a Cyclic Module?
This looks like the kind of thing that one might be able to prove by filtering $U$ by word-length over $g$ and then passing to the associated graded ring. The idea is that this would reduce the proble …
- 3,545
3
votes
Homology of solvable (nilpotent) Lie algebras
To fill out my comment with a partial answer to the question.
Note that given any (left) $\mathfrak{g}$-module $V$ one can compute $H_i(\mathfrak{g},V)$ as $\mathrm{Tor}_i^{U(\mathfrak{g})}(\mathbb{C …
- 3,545
3
votes
Homology of solvable (nilpotent) Lie algebras
This is an attempt to prove the (refined) conjecture I made in the comments of my previous answer. Let $\mathfrak{g}$ be a f.d soluble Lie algebra over $\mathbb{C}$. Let $\mathfrak{n}$ be its derived …
- 3,545