#### Some homological properties of skew P BW extensions arising in non-commutative algebraic geometry

###### Autor: Helbert Javier Venegas Ramirez

###### Coautor(es): JosÃ© Oswaldo Lezama-Helbert Javier Venegas

###### In this short talk we study for the skew P BW (PoincarÂ´e-Birkhoff-Witt) extensions some homological
properties arising in non-commutative algebraic geometry, namely, Auslander-Goresntein regularity,
Cohen-Macaulayness and strongly noetherianity. Skew P BW extensions include a considerable
number of non-commutative rings of polynomial type such that classical P BW 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.