Applying the results and techniques of skew PBW extensions developed in the specialized literature, in
the present project we want to investigate connections between skew PBW extensions and some rings
and algebras arising from non-commutative algebraic geometry. The objects to be considered here
correspond to some of new trends in Noncommutative Algebra and Algebraic Geometry identified
recently (October-November, 2012) in a workshop organized by MSRI at Banff
International Research Station (BIRS) in Alberta, Canada. Three of most relevant topics studied in this workshop were: (i) Hopf algebra actions on filtered algebras (ii)
Auslander-Gorenstein rings, Artin-Schelter regular algebras and W-algebras (iii) Skew Calabi-Yau
algebras. We will investigate the relationship between skew PBW extensions and these recent classes of rings and algebras. |