Dirac Operators on Quadratic Lie Superalgebras  

作　　者：Yi Fang KANG Zhi Qi CHEN 

机构地区：[1]Institute of Mathematics and Physics,Central South University of Forestry and Technology,Changsha 410004,P.R.China [2]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第8期1229-1253,共25页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11571182 and 11931009);the Talents Foundation of Central South University of Forestry and Technology(Grant No.104-0089);Natural Science Foundation of Tianjin(Grant No.19JCYBJC30600)。

摘　　要：Assume thatτis 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 nondegenerate super-symmetric bilinear form,and v:τ→osp(p)is a homomorphism of Lie superalgebras.In this paper,we give a necessary and sufficient condition forτ■p to be a quadratic Lie superalgebra.Then,we define the cubic Dirac operator D(g,τ)on g and give a formula of(D(g,τ))^(2).Finally,we get the Vogan’s conjecture for quadratic Lie superalgebras by D(g,τ).

关 键 词：Quadratic Lie superalgebra exterior algebra Clifford algebra Dirac operator 

分 类 号：O152.5[理学—数学]