Non-weight modules over the Block type algebra B'(p, q)

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. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we investigate the non-weight modules over the Block type algebra B'(p, q), and construct a family of such irreducible modules. We determine their isomorphism classes and demonstrate that these modules exhaust the B'(p, q) modules that are U(h)-free modules with rank 1, where h represents the Cartan subalgebra.