2 results
BGG reciprocity for current algebras
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 7 / July 2015
- Published online by Cambridge University Press:
- 09 February 2015, pp. 1265-1287
- Print publication:
- July 2015
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- Article
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The Second Cohomology of Current Algebras of General Lie Algebras
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- Journal:
- Canadian Journal of Mathematics / Volume 60 / Issue 4 / 01 August 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 892-922
- Print publication:
- 01 August 2008
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- Article
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- You have access
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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.
