On modular representations of finite-dimensional Lie superalgebras

YANG Heng-yun; YAO Yu-feng

doi:10.3969/j.issn.1000-5641.2017.03.001

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May 2017

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

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

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On modular representations of finite-dimensional Lie superalgebras

doi: 10.3969/j.issn.1000-5641.2017.03.001

YANG Heng-yun,
YAO Yu-feng^,

Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

More Information

Corresponding author: 姚裕丰, 男, 副教授, 研究方向为李理论及表示理论.E-mail:yfyao@shmtu.edu.cn
Received Date: 2017-03-01
Publish Date: 2017-05-25

Abstract

Abstract

In this paper, we studied representations of finite-dimensional Lie superalgebras over an algebraically closed field $\mathbb{F}$ of characteristic p > 2. It was shown that simple modules of a finite-dimensional Lie superalgebra over $\mathbb{F}$ 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 ${\mathfrak{g}}$, and defined a restricted Lie super subalgebra, then obtained a bijection between the isomorphism classes of simple modules of ${\mathfrak{g}}$ and those of this restricted subalgebra. These results are generalization of the corresponding ones in Lie algebras of prime characteristic.
- Lie superalgebra,
- representation,
- p-envelope,
- p-character

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References(20)

References

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