Central extensions of current algebras

Zusmanovich, Paul

doi:10.1090/S0002-9947-1992-1069751-2

Central extensions of current algebras
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Trans. Amer. Math. Soc. 334 (1992), 143-152 Request permission

Erratum: Trans. Amer. Math. Soc. 362 (2010), 5601-5603.

Abstract:

The second cohomology group of Lie algebras of kind $L \otimes U$ with trivial coefficients is investigated, where $L$ admits a decomposition with one-dimensional root spaces and $U$ is an arbitrary associative commutative algebra with unit. This paper gives a unification of some recent results of C. Kassel and A. Haddi and provides a determination of central extensions of certain modular semisimple Lie algebras.

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The modular simple Lie algebras with a solvable maximal subalgebra

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