Down-Up Algebras and Representation Theory

1999/03/20 by Paula A. A. B. Carvalho, Carvalho, Paula A. A. B., Ian M. Musson +1
Computer Science · Mathematics · #16P40 #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #math.RT #msc:16P40

paper · pdf · doi:10.48550/arxiv.math/9903120

23 pages, AMS Latex

arxiv created 1999/03/20 · openalex publication_date 1999/03/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A class of algebras called down-up algebras was introduced by G. Benkart and T. Roby. 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.

Related

• Classification of factorial generalized down-up algebras
• Down-up Algebras
• Stable rank of down-up algebras
• Primitive ideals of noetherian generalized down-up algebras
• Automorphisms of Generalized Down-Up Algebras