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

TL;DR

This paper investigates the structure of a class of not-finitely graded Lie algebras connected to generalized Heisenberg-Virasoro algebras, focusing on derivations, automorphisms, and cohomology groups.

Contribution

It provides a detailed analysis of derivation algebras, automorphism groups, and second cohomology groups for these specific Lie algebras, which were not previously characterized.

Findings

Determined derivation algebras of the studied Lie algebras.

Computed automorphism groups for these Lie algebras.

Established the second cohomology groups, revealing their extension properties.

Abstract

In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.