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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Central extensions of nonsymmetrizable Kac-Moody algebras over commutative algebras
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by Yun Gao PDF
Proc. Amer. Math. Soc. 121 (1994), 67-76 Request permission

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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Additional 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