## 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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## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**121**(1994), 67-76 - MSC: Primary 17B67; Secondary 17B65
- DOI: https://doi.org/10.1090/S0002-9939-1994-1185261-3
- MathSciNet review: 1185261