All Questions

I learned that the Hochschild cohomology of an associative algebra $A$ with a bimodule $M$ is defined using the cochain \begin{align*} \cdots \rightarrow C^n(A,M) \stackrel{d^n}{\longrightarrow} C^{n+...

The way I learned Lie algebra cohomology in the context of Lie groups was a direct construction: one defines the Chevalley-Eilenberg complex with coefficients in a vector space $V$ (we assume the real ...

The Witt algebra (denoted by $W$) is an infinite dimensional Lie algebra as: $[L_{m},L_{n}]=(m-n)L_{m+n}; \,\,\,\ m, n\in \mathbb{Z}$. I am looking for second adjoint cohomology $H^{2}(W_{1}\oplus ...

Let $L$ be a (differential) graded Lie algebra over a field $k$ of characteristic 0, and let $UL$ be the universal enveloping algebra of $L$. The inclusion $L\hookrightarrow UL$ induces a morphism of ...