On representations of the filiform Lie superalgebra Lm, n

JOURNAL OF GEOMETRY AND PHYSICS

卷:97

Article

Wang, Qi¹  Chen, Hongjia²  Liu, Wende^1,3 

[1] Harbin Inst Technol, Dept Math, Harbin 150006, Peoples R China

[2] Chinese Acad Sci, Univ Sci & Technol China, Sch Math Sci, Key Lab Wu WenTsun Math, Hefei 230026, Peoples R China

[3] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Peoples R China

关键词: Filiform Lie superalgebra;    Minimal faithful representation;    Jordan form;   

DOI  :  10.1016/j.geomphys.2015.07.012

来源: Elsevier

【 摘 要 】

In this paper, we study the representations for the filiform Lie superalgebras L-m,L-n, a particular class of nilpotent Lie superalgebras. We determine the minimal dimension of a faithful module over L-m,L-n using the theory of linear algebra. In addition, using the method of Feingold and Frenkel (1985), we construct some finite and infinite dimensional modules over L-m,L-n on the Grassmann algebra and the mixed Clifford-Weyl algebra. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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