Down-up algebras and their representation theory

Abstract

A class of algebras called down-up algebras was introduced by G. Benkart and T. Roby (1998, J. Algebra209, 305-344). We classify the finite dimensional simple modules over Noetherian down-up algebras and show that in some cases every finite dimensional module is semisimple. We also study the question of when two down-up algebras are isomorphic. © 2000 Academic Press.