Second cohomology groups and left-symmetric algebraic structures of the generalized loop Heisenberg-Virasoro algebra

TL;DR

This paper investigates the second cohomology groups and left-symmetric algebraic structures of the generalized loop Heisenberg-Virasoro algebra, expanding understanding of its algebraic properties using Witt algebras.

Contribution

It provides a detailed description of the second cohomology group and left-symmetric algebra structures for this algebra, building on the structure of Witt subalgebras.

Findings

Describes the second cohomology group of the algebra.

Classifies left-symmetric algebra structures on the algebra.

Utilizes Witt algebras as subalgebras in the analysis.

Abstract

This is the second paper in our series of papers dedicated to the study of the generalized loop Heisenberg-Virasoro algebra. The first paper is dedicated to the study of maps on the generalized loop Heisenberg-Virasoro algebra, including derivations, $2$-local derivations, biderivations the automorphism groups. The present paper is dedicated to the study of the second cohomology groups and left-symmetric algebraic structures on the generalized loop Heisenberg-Virasoro algebra. We describe the second cohomology group and left-symmetric algebra structures on the generalized loop Heisenberg-Virasoro algebra by use of the Witt algebras being Lie subalgebra of the generalized loop Heisenberg-Virasoro algebra up to isomorphism.