Noetherian down-up algebras

Authors
Kirkman, E Musson, IM Passman, DS
Citation
E. Kirkman et al., Noetherian down-up algebras, P AM MATH S, 127(11), 1999, pp. 3161-3167
Citations number
11
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
127
Issue
11
Year of publication
1999
Pages
3161 - 3167
Database
ISI
SICI code
0002-9939(199911)127:11<3161:NDA>2.0.ZU;2-Z
Abstract
Down-up algebras A = A(alpha, beta, gamma) were introduced by G. Benkart an d T. Roby to better understand the structure of certain posets. In this pap er, we prove that beta not equal 0 is equivalent to A being right (or left) Noetherian, and also to A being a domain. Furthermore, when this occurs, w e show that A is Auslander-regular and has global dimension 3.