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 bil...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).展开更多
Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Ba...Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.展开更多
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)。
文摘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).
基金Supported by National Natural Science Foundation of China(Grant No.11401425)
文摘Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.
