Classification of irreducible Harish-Chandra modules over gap-p Virasoro algebras

Abstract

We prove that any irreducible Harish-Chandra module for a class of Lie algebras, which we call gap-p Virasoro algebras, must be a highest weight module, a lowest weight module, or a module of intermediate series. These algebras are closely related to the Heisenberg-Virasoro algebra and the algebra of derivations over a quantum torus. They also contain subalgebras which are isomorphic to the Virasoro algebra Vir, but graded by pZ (unlike Vir by Z).