Down–Up Algebras and Their Representation Theory

By Paula Carvalho, I. Musson. 2000

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Abstract A class of algebras called down–up algebras was introduced by G. Benkart and T. Roby (1998, J. Algebra 209 , 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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