Structures of generalized loop super-Virasoro algebras

Abstract

The structure theory of a class of generalized loop super-Virasoro algebras is studied in this paper. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of generalized loop centerless supper-Virasoro algebras are determined completely.

Loop Virasoro Lie conformal superalgebra

“…The object investigated in this paper is a Lie conformal superalgebra closed related to the loop super-Virasoro algebra sl whose structures were studied in [7]. It is defined as a infinitedimensional Lie superalgebra with a basis {L α,i , G µ,j | α, i, j ∈ Z, µ ∈ 1 2 + Z} satisfying the following commutation relations:…”

Structures of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras

“…The theory of Lie superalgebras plays a prominent role in modern mathematics and physics. In recent years, structures of all kinds of Lie superalgebras have aroused many scholars' great interests (see, e.g., [2,7,9,18]). In this paper, 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).…”

“…It plays a very important role in mathematics and physics. The structure and representation theories of (generalized) super-Virasoro algebra have been extensively undertaken by many authors (see, e.g., [2,9,[11][12][13][14]17,20,21]). The generalized super-Virasoro algebra SV ir[Γ, s] is a Lie superalgebra whose even part SV0 has a basis {L α , C | α ∈ Γ} and odd part SV1 has a basis {G µ | µ ∈ Γ + s}, equipped with the following Lie super-brackets:…”