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

TL;DR

This paper explores the detailed structure of a class of not-finitely graded Lie superalgebras connected to generalized super-Virasoro algebras, including derivations, automorphisms, and cohomology.

Contribution

It provides a complete determination of derivation algebras, automorphism groups, and second cohomology groups for these Lie superalgebras, advancing their structural understanding.

Findings

Derived the full derivation algebras

Determined automorphism groups

Computed second cohomology groups

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.