Mathematics

On modular representations of finite-dimensional Lie superalgebras

  • YANG Heng-yun ,
  • YAO Yu-feng
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  • Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

Received date: 2017-03-01

  Online published: 2017-05-18

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.

Cite this article

YANG Heng-yun , YAO Yu-feng . On modular representations of finite-dimensional Lie superalgebras[J]. Journal of East China Normal University(Natural Science), 2017 , (3) : 1 -19 . DOI: 10.3969/j.issn.1000-5641.2017.03.001

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