Bernstein inequality and functional equations for certain quantum Weyl algebras (Q1373484)

The author derives a Bernstein-type inequality giving a lower bound on the GK dimension of any simple module over either of two quantum analogues of the Weyl algebra, one introduced by \textit{T. Hayashi} in [Commun. Math. Phys. 127, 129-144 (1990; Zbl 0701.17008)] and the other by \textit{M. Akhavizadegan} and \textit{D. A. Jordan} in [Glasg. Math. J. 38, 283-297 (1996; Zbl 0881.16012)]; actually, the author works with a localization of the Akhavizadegan- Jordan algebra. The methods are largely the original ones of Bernstein, adapted to the quantized setting. The author also derives a functional equation for holonomic modules over these algebras and shows that they are Auslander regular and Cohen-Macaulay.