The Second Cohomology of Current Algebras of General Lie Algebras

Neeb, Karl-Hermann ; Wagemann, Friedrich

Canadian journal of mathematics, Tome 60 (2008) no. 4, pp. 892-922

Résumé

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

Détail

DOI : 10.4153/CJM-2008-038-6

Mots-clés : 17B56, 17B65, current algebra, Lie algebra cohomology, Lie algebra homology, invariant bilinear form, central extension

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