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Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry
Discussiones Mathematicae. General Algebra and Applications, Tome 37 (2017) no. 1, pp. 45-57

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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 
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Lezama, Oswaldo. Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry. Discussiones Mathematicae. General Algebra and Applications, Tome 37 (2017) no. 1, pp. 45-57. http://geodesic.mathdoc.fr/item/DMGAA_2017_37_1_a3/