Low-dimensional cohomology of Lie superalgebra slm|n with coefficients in Witt or Special superalgebras

Liping Sun; Wende Liu; Boying Wu

doi:10.1016/j.indag.2013.07.006

Low-dimensional cohomology of Lie superalgebra slm|n with coefficients in Witt or Special superalgebras

Liping Sun
, Wende Liu^*
, Boying Wu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Harbin University of Science and Technology
Harbin Normal University

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

4 Scopus citations

Abstract

Over a field of characteristic p>. 2, the Witt superalgebras are viewed as modules of the special linear Lie superalgebra slm|n by means of the adjoint representation. The low-dimensional cohomology groups of slm|n with coefficients in Witt superalgebras are computed by virtue of the direct sum decomposition of submodules and the weight space decompositions of these submodules relative to the standard Cartan subalgebra of slm|n. Then we are able to obtain the low-dimensional cohomology groups of slm|n with coefficients in Special superalgebras, which are slm|n-submodules of Witt superalgebras.

Original language	English
Pages (from-to)	59-77
Number of pages	19
Journal	Indagationes Mathematicae
Volume	25
Issue number	1
DOIs	https://doi.org/10.1016/j.indag.2013.07.006
State	Published - 5 Jan 2014

Keywords

Cohomology
Special superalgebra
Witt superalgebra

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10.1016/j.indag.2013.07.006

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abstract = "Over a field of characteristic p>. 2, the Witt superalgebras are viewed as modules of the special linear Lie superalgebra slm|n by means of the adjoint representation. The low-dimensional cohomology groups of slm|n with coefficients in Witt superalgebras are computed by virtue of the direct sum decomposition of submodules and the weight space decompositions of these submodules relative to the standard Cartan subalgebra of slm|n. Then we are able to obtain the low-dimensional cohomology groups of slm|n with coefficients in Special superalgebras, which are slm|n-submodules of Witt superalgebras.",

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author = "Liping Sun and Wende Liu and Boying Wu",

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AU - Sun, Liping

AU - Liu, Wende

AU - Wu, Boying

PY - 2014/1/5

Y1 - 2014/1/5

N2 - Over a field of characteristic p>. 2, the Witt superalgebras are viewed as modules of the special linear Lie superalgebra slm|n by means of the adjoint representation. The low-dimensional cohomology groups of slm|n with coefficients in Witt superalgebras are computed by virtue of the direct sum decomposition of submodules and the weight space decompositions of these submodules relative to the standard Cartan subalgebra of slm|n. Then we are able to obtain the low-dimensional cohomology groups of slm|n with coefficients in Special superalgebras, which are slm|n-submodules of Witt superalgebras.

AB - Over a field of characteristic p>. 2, the Witt superalgebras are viewed as modules of the special linear Lie superalgebra slm|n by means of the adjoint representation. The low-dimensional cohomology groups of slm|n with coefficients in Witt superalgebras are computed by virtue of the direct sum decomposition of submodules and the weight space decompositions of these submodules relative to the standard Cartan subalgebra of slm|n. Then we are able to obtain the low-dimensional cohomology groups of slm|n with coefficients in Special superalgebras, which are slm|n-submodules of Witt superalgebras.

KW - Cohomology

KW - Special superalgebra

KW - Witt superalgebra

UR - https://www.scopus.com/pages/publications/84888200023

U2 - 10.1016/j.indag.2013.07.006

DO - 10.1016/j.indag.2013.07.006

M3 - 文章

AN - SCOPUS:84888200023

SN - 0019-3577

VL - 25

SP - 59

EP - 77

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

Low-dimensional cohomology of Lie superalgebra slm|n with coefficients in Witt or Special superalgebras

Abstract

Keywords

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