Dirac Operators on Quadratic Lie Superalgebras

被引：0

作者：

Kang, Yi Fang ^{[1
]}

Chen, Zhi Qi ^{[2
,3
]}

机构：

[1] Cent South Univ Forestry & Technol, Inst Math & Phys, Changsha 410004, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2021年 / 37卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Quadratic Lie superalgebra; exterior algebra; Clifford algebra; Dirac operator; REPRESENTATIONS; MULTIPLETS; COHOMOLOGY; CONJECTURE; ALGEBRA;

D O I：

10.1007/s10114-021-0556-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Assume that r is a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form, p is a finite dimensional complex super vector space with a non-degenerate super-symmetric bilinear form, and nu : r -> osp(p) is a homomorphism of Lie superalgebras. In this paper, we give a necessary and sufficient condition for r circle plus p to be a quadratic Lie superalgebra. Then, we define the cubic Dirac operator D(g, r) on g and give a formula of (D(g, r))(2.) Finally, we get the Vogan's conjecture for quadratic Lie superalgebras by D(g, r).

引用

页码：1229 / 1253

页数：25

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