Central extensions of nonsymmetrizable Kac-Moody algebras over commutative algebras

Gao, Yun

doi:10.1090/S0002-9939-1994-1185261-3

Central extensions of nonsymmetrizable Kac-Moody algebras over commutative algebras
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by Yun Gao

Proc. Amer. Math. Soc. 121 (1994), 67-76

DOI: https://doi.org/10.1090/S0002-9939-1994-1185261-3

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Abstract:

For a commutative algebra R over a field k of characteristic zero and a nonsymmetrizable Kac-Moody algebra $g(A)$, we prove that the Lie algebra ${g_R}(A) = R{ \otimes _k}g(A)$ is centrally closed. Consequently, we get a characterization of the symmetrizability of $g(A)$ by the second homology group of the Kac-Moody algebra over Laurent polynomials. Also a presentation of ${g_R}(A)$ is given when A is of nonaffine type.

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