Homogeneous PBW Deformation for Artin–schelter Regular Algebras

Abstract

We introduce a method named homogeneous PBW deformation that preserves the regularity and some other homological properties for multigraded algebras. The method is used to produce Artin-Schelter regular algebras without the hypothesis on grading.2010 Mathematics subject classification: primary 16E65; secondary 16W50, 14A22.

Nakayama automorphisms of PBW deformations and Hopf actions

“…Example 2.10. Starting with graded Down-Up algebras, there are four classes of Artin-Schelter regular algebras which are homogeneous PBW deformations of graded Down-Up algebras (see [21,Example 5.3]). The following are two special cases:…”

Behavior of the Auslander condition with respect to regradings

“…Remark. In the work [18], a method called "Homogeneous PBW deformation" is developed to construct new Z-graded Artin-Schelter regular algebras from multi-graded old ones by adding to each relation a tail of the same Z-degree but different multi-degree. It is the technique of multi-filtration to assure that this method actually preserves nice ring-theoretic and homological properties.…”