On modular representations of finite-dimensional Lie superalgebras

doi:10.3969/j.issn.1000-5641.2017.03.001

Abstract

Abstract: In this paper, we studied representations of finite-dimensional Lie superalgebras over an algebraically closed field F of characteristic p > 2. It was shown that simple modules of a finite-dimensional Lie superalgebra over F are finite-dimensional, and there exists an upper bound on the dimensions of simple modules. Moreover, a finite-dimensional Lie superalgebra can be embedded into a finite-dimensional restricted Lie superalgebra. We gave a criterion on simplicity of modules over a finite-dimensional restricted Lie superalgebra g, and defined a restricted Lie super subalgebra, then obtained a bijection between the isomorphism classes of simple modules of g and those of this restricted subalgebra. These results are generalization of the corresponding ones in Lie algebras of prime characteristic.

Key words: Lie superalgebra, representation, p-envelope, p-character

CLC Number:

O152.5

YANG Heng-yun, YAO Yu-feng. On modular representations of finite-dimensional Lie superalgebras[J]. Journal of East China Normal University(Natural Sc, 2017, (3): 1-19.

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