Abstract
This paper is devoted to investigating the structure theory of a class of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we completely determine the derivation algebras, the automorphism groups and the second cohomology groups of these Lie superalgebras.
Highlights
For the readers’ convenience, we give some notations used in this paper
The theory of Lie superalgebras plays a prominent role in modern mathematics and physics
We shall investigate the structure theory of a class of not-finitely graded Lie superalgebras related to the generalized super-Virasoro algebras
Summary
For the readers’ convenience, we give some notations used in this paper. Let ⊆ Γ be an additive subgroup of and s∈ such that 2sΓ. Let L be a Lie superalgebra, and denote by hg(L) the set of all homogeneous elements of L. We shall investigate the structure theory of a class of not-finitely graded Lie superalgebras related to the generalized super-Virasoro algebras (namely, derivations, automorphisms, 2-cocycles). The generalized super-Virasoro algebra SVir[Γ, s] is a Lie superalgebra whose even part SV0 has a basis {Lα, C|α∈Γ} and odd part SV1 has a basis {Gμ|μ∈Γ+s}, equipped with the following Lie superbrackets:. We will consider the following Lie superalgebra, called not-finitely graded generalized super-Virasoro algebra [Γ, s], which has a basis {Lα,i, Gμ,j||α∈Γ,μ∈s+Γ,i, j∈ +}, and satisfies the following relations:. In [5,19] some authors studied some structures of not-finitely graded Lie algebras. The quotient space H2(L, )=C2(L, )/ B2(L, ) is called the 2-cohomology group of L
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