Non-weight modules over the Block type algebra [formula omitted

Abstract

In this paper, we study the non-weight modules over the Block type algebra B′(p,q), where p(≠0), q are some complex numbers. We construct a family of such irreducible modules, determine their isomorphism classes, and show that they exhaust the B′(p,q)-modules which are U(h)-free modules of rank 1, where h is the Cartan subalgebra.