A note on restricted representations of the Witt superalgebras

Yufeng Yao; Bin Shu

doi:10.1007/s11401-013-0800-1

A note on restricted representations of the Witt superalgebras

Yufeng Yao^*
, Bin Shu

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai Maritime University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let F be an algebraically closed field of prime characteristic p > 3, and W(n) the Witt superalgebra over F, which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates. The dimensions of simple atypical modules in the restricted supermodule category for W(n) are precisely calculated in this paper, and thereby the dimensions of all simple modules can be precisely given. Moreover, the restricted supermodule category for W(n) is proved to have one block.

Original language	English
Pages (from-to)	921-926
Number of pages	6
Journal	Chinese Annals of Mathematics. Series B
Volume	34
Issue number	6
DOIs	https://doi.org/10.1007/s11401-013-0800-1
State	Published - Nov 2013

Keywords

Atypical weight
Restricted Lie superalgebra
Restricted representation
Witt superalgebra

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10.1007/s11401-013-0800-1

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AB - Let F be an algebraically closed field of prime characteristic p > 3, and W(n) the Witt superalgebra over F, which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates. The dimensions of simple atypical modules in the restricted supermodule category for W(n) are precisely calculated in this paper, and thereby the dimensions of all simple modules can be precisely given. Moreover, the restricted supermodule category for W(n) is proved to have one block.

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KW - Restricted Lie superalgebra

KW - Restricted representation

KW - Witt superalgebra

UR - https://www.scopus.com/pages/publications/84887537926

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ER -

A note on restricted representations of the Witt superalgebras

Abstract

Keywords

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