Stable rank of down-up algebras

2017/07/20 by Gallego, Claudia, Solotar, Andrea
#19A13 #19B10. Secondary: 16P60 #FOS: Mathematics #Primary: 16D40 #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1707.06687

Abstract

We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute the stable rank of these algebras using Stafford's Stable Range Theorem and Kmax dimension.

Related

• Down-Up Algebras and Representation Theory
• The Stable Rank of C*-modules
• Primitive ideals of noetherian generalized down-up algebras
• Classification of factorial generalized down-up algebras
• Stably Noetherian Algebras of Polynomial Growth