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arXiv · 1606.01546

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

Oswaldo Lezama·Helbert Venegas
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Abstract

In this short paper we study for the skew PBW (Poincar\'e-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. For some key examples we present the parametrization of its point modules.

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Oswaldo Lezama, Helbert Venegas. 2016-06-05. Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry. https://arxiv.org/abs/1606.01546

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