Down-up algebras over a polynomial base ring K[t1, . . . , tn]
Document Type
Article
Publication Date
3-1-2016
Abstract
We study a class of down-up algebras A(?, ?, ?) defined over a polynomial base ring K[t1, . . . , tn] and establish several analogous results. We first construct a K-basis for the algebra A(?, ?, ?). As an application, we completely determine the center of A(?, ?, ?) when charK = 0, and prove that the Gelfand-Kirillov dimension of A(?, ?, ?) is n+ 3. Then, we prove that A(?, ?, ?) is a noetherian domain if and only if 0, and A(?, ?, ?) is Auslander-regular when 0. We show that the global dimension of A(?, ?, ?) is n + 3, and A(?, ?, ?) is a prime ring except when á = â = ö = 0. Finally, we obtain some results on the Krull dimensions, isomorphisms and automorphisms of A(?, ?, ?).
Recommended Citation
Tang, Xin, "Down-up algebras over a polynomial base ring K[t1, . . . , tn]" (2016). College of Health, Science, and Technology. 291.
https://digitalcommons.uncfsu.edu/college_health_science_technology/291