Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two

TL;DR

This paper classifies a specific family of non-weight modules over a generalized Heisenberg-Virasoro algebra of rank two, providing explicit constructions and showing they encompass all modules with certain free module properties.

Contribution

It constructs and classifies all irreducible non-weight modules of rank one over the generalized Heisenberg-Virasoro algebra of rank two.

Findings

Constructed a family of irreducible modules.

Determined isomorphism classes of these modules.

Proved these modules exhaust all free rank-one modules over the Cartan subalgebra.

Abstract

In this paper, we study a class of non-weight modules over the generalized Heisenberg-Virasoro algebra of rank two $\widetilde{L}(p_1, p_2)$. We construct a family of irreducible $\widetilde{L}(p_1, p_2)$-modules, determine the isomorphism classes and show that these modules exhaust all the $\widetilde{L}(p_1, p_2)$-modules that are free modules of rank one over the Cartan subalgebra.