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The second cohomology of current algebras of general Lie algebras

Karl-Hermann Neeb·Friedrich Wagemann
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Abstract

Let $A$ be a unital commutative associative algebra over a field of characteristic zero, $\k$ be a Lie algebra, and $\z$ a vector space, considered as a trivial module of the Lie algebra $\g := A \otimes \k$. In this paper we give a description of the cohomology space $H^2(\g,\z)$ in terms of well accessible data associated to $A$ and $\k$. We also discuss the topological situation, where $A$ and $\k$ are locally convex algebras.

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Karl-Hermann Neeb, Friedrich Wagemann. 2008-04-29. The second cohomology of current algebras of general Lie algebras. https://arxiv.org/abs/math/0511260

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