Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry

Abstract

In this short paper we study for the skew PBW (Poincar-Birkhoff-Witt) extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly noetherianity. Skew PBW extensions include a considerable number of non-commutative rings of polynomial type such that classical PBW extensions, quantum polynomial rings, multiplicative analogue of the Weyl algebra, some Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in 3 variables, among many others. Parametrization of the point modules of some examples is also presented.

Keywords

• auslander regularity condition
• cohen-macaulay rings
• strongly noetherian algebras
• skew pbw extensions
• filtered-graded rings
• point modules
• primary: 16s38
• secondary: 16w50, 16s80, 16s36