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Bernstein inequality and functional equations for certain quantum Weyl algebras. (Inégalité de Bernstein et équations fonctionnelles pour certaines algèbres de Weyl quantiques.) (French) Zbl 0895.17007
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 T. Hayashi in [Commun. Math. Phys. 127, 129-144 (1990; Zbl 0701.17008)] and the other by M. Akhavizadegan and 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.

17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)