The second cohomology of current algebras of general Lie algebras

Details The second cohomology of current algebras of general Lie algebras The second cohomology of current algebras of general Lie algebras

2005-11-10

arxiv.org/abs/math/0511260v2

Mathematics

Rings and Algebras

Some minor corrections have been made in this version

Scientific paper

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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