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Central extensions of nonsymmetrizable Kac-Moody algebras over commutative algebras

Author: Yun Gao
Journal: Proc. Amer. Math. Soc. 121 (1994), 67-76
MSC: Primary 17B67; Secondary 17B65
MathSciNet review: 1185261
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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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Article copyright: © Copyright 1994 American Mathematical Society

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