Down-up algebras over a polynomial base ring K[t(1),..., t(n)]

作者：Tang Xin^*

来源：Journal of Algebra and Its Applications, 2016, 15(2): 1650024.

DOI：10.1142/S0219498816500249

• Down-up algebras
• global dimension
• Krull dimension
• algebra automorphism

We study a class of down-up algebras A(alpha, beta, phi) defined over a polynomial base ring K[t(1),..., t(n)] and establish several analogous results. We first construct a K-basis for the algebra A(alpha, beta, phi). As an application, we completely determine the center of A(alpha, beta, phi) when char K = 0, and prove that the Gelfand-Kirillov dimension of A(alpha, beta, phi) is n + 3. Then, we prove that A(alpha, beta, phi) is a noetherian domain if and only if beta not equal 0, and A(alpha, beta, phi) is Auslander-regular when beta not equal 0. We show that the global dimension of A(alpha, beta, phi) is n + 3, and A(alpha, beta, phi) is a prime ring except when alpha = beta = phi = 0. Finally, we obtain some results on the Krull dimensions, isomorphisms and automorphisms of A(alpha, beta, phi).

• 出版日期2016-3