English

PBW deformations of Artin-Schelter regular algebras

Rings and Algebras 2017-12-06 v2

Abstract

We consider algebras that can be realized as PBW deformations of (Artin-Schelter) regular algebras. This is equivalent to the homogenization of the algebra being regular. It is shown that the homogenization, when it is a geometric algebra, contains a component whose points are in 1-1 correspondence with the simple modules of the deformation. We classify all PBW deformations of 2-dimensional regular algebras and give examples of 3-dimensional deformations. Other properties, such as the skew Calabi-Yau property and closure under tensor products, are considered.

Keywords

Cite

@article{arxiv.1210.0861,
  title  = {PBW deformations of Artin-Schelter regular algebras},
  author = {Jason Gaddis},
  journal= {arXiv preprint arXiv:1210.0861},
  year   = {2017}
}

Comments

Editing throughout. Propositions 2.5 and 3.7 corrected. Updated Section 3 on skew CY-property