Restricted representations of the Witt superalgebras

Bin Shu; Chaowen Zhang

doi:10.1016/j.jalgebra.2010.04.032

Restricted representations of the Witt superalgebras

Bin Shu^*
, Chaowen Zhang

^*Corresponding author for this work

School of Mathematical Sciences

China University of Mining and Technology

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

33 Scopus citations

Abstract

Let k be an algebraically closed field of characteristic p>3, and W(n) the superversion of the Witt algebra over k, i.e. the Lie superalgebra of superderivations of the Grassmann algebra of rank n over k. The simple modules and projective indecomposable modules in the restricted supermodule category for W(n) are studied. The character formulas for such simple modules are given, and the Cartan invariants for this category are presented.

Original language	English
Pages (from-to)	652-672
Number of pages	21
Journal	Journal of Algebra
Volume	324
Issue number	4
DOIs	https://doi.org/10.1016/j.jalgebra.2010.04.032
State	Published - 15 Aug 2010

Keywords

Cartan invariants
Character formulas
Irreducible restricted supermodules
Kac modules
Witt superalgebras

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10.1016/j.jalgebra.2010.04.032

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abstract = "Let k be an algebraically closed field of characteristic p>3, and W(n) the superversion of the Witt algebra over k, i.e. the Lie superalgebra of superderivations of the Grassmann algebra of rank n over k. The simple modules and projective indecomposable modules in the restricted supermodule category for W(n) are studied. The character formulas for such simple modules are given, and the Cartan invariants for this category are presented.",

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AB - Let k be an algebraically closed field of characteristic p>3, and W(n) the superversion of the Witt algebra over k, i.e. the Lie superalgebra of superderivations of the Grassmann algebra of rank n over k. The simple modules and projective indecomposable modules in the restricted supermodule category for W(n) are studied. The character formulas for such simple modules are given, and the Cartan invariants for this category are presented.

KW - Cartan invariants

KW - Character formulas

KW - Irreducible restricted supermodules

KW - Kac modules

KW - Witt superalgebras

UR - https://www.scopus.com/pages/publications/84861704468

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M3 - 文章

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SN - 0021-8693

VL - 324

SP - 652

EP - 672

JO - Journal of Algebra

JF - Journal of Algebra

IS - 4

ER -

Restricted representations of the Witt superalgebras

Abstract

Keywords

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