Dirac Operators on Quadratic Lie Superalgebras

• 作者: Yi Fang KANG Zhi Qi CHEN
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（8）
• 页码范围: 1229-1253
• 页数: 25页
• 语种: 英文

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 v:t → osp(p)is a homomorphism of Lie superalgebras.In this paper,we give a necessary and sufficient condition for t ⊕ p to be a quadratic Lie superalgebra.Then,we define the cubic Dirac operator D(g,t)on g and give a formula of(D(g,t))2.Finally,we get the Vogan's conjecture for quadratic Lie superalgebras by D(g,t).