All Questions
7 questions
4
votes
1
answer
133
views
Second cohomology group of the contact Lie algebra $K_3$
Let $F$ be a field of characteristic zero and, for all $n>0$, consider the contact Lie algebra $K_{2n+1}$. It follows from Corollary 3 of the paper [V. Guillemin - S. Shnider: Some stable results ...
- 630
3
votes
1
answer
129
views
Schur multiplier of finite-dimensional simple Lie algebras in positive characteristic
The Schur multipliers of finite simple groups are known and easily accessible:
https://en.wikipedia.org/wiki/List_of_finite_simple_groups
Moreover, as a consequence of the second Whitehead's Lemma, if ...
- 630
3
votes
0
answers
117
views
Twisting an L_{\infty} module quasi-isomorphism with a sufficiently small Maurer-Cartan element
I was wondering if someone could help me understand this result, or point me towards a reference. Suppose that $M$ and $N$ are $L_{\infty}$ modules over a dgla $L$. Suppose that $\phi: M \rightarrow N$...
- 295
4
votes
0
answers
75
views
Lie algebra "semi" coinvariants
In the process of my research, I've come across the need to understand the following construction:
Let $\mathfrak{g}$ be a (finite-dimensional) complex Lie algebra, $\beta\in \mathfrak{g}^*$ a Lie ...
- 3,079
2
votes
0
answers
55
views
Free resolutions of universal enveloping algebras for simple, finite dimensional Lie algebras
I'm currently studying Anick's resolution on the context of universal enveloping algebras for certain Lie algebras, namely some of the smallest cases: $A_1,A_2,A_3,B_2,G_2$, and so on.
What are some ...
1
vote
1
answer
129
views
Lie algebra cohomology: $H^i(R,V)=H^i(R,V^R)$ with $R$ reductive and $V$ an $R$-module
Let $R$ be a reductive, finite-dimensional Lie algebra over a field of characteristic 0, and let $V$ be a semisimple $R$-module (also finite dimensional). I have seen a reference to the fact that $H^i(...
- 13
9
votes
3
answers
1k
views
Poincaré duality for (co)homology of Lie algebras?
Let $R$ be a commutative ring and $\mathfrak{g}$ a Lie $R$-algebra that has an $R$-module basis with $n$ elements.
In Algebra, Geometry, and Software Systems by Joswig & Takayama on p.200, it ...
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