PBW deformations of Artin-Schelter regular algebras

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.

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

References in corpus (3)

• Skew Calabi-Yau Algebras and Homological Identities
• Two-generated algebras and standard-form congruence
• Twisted Calabi-Yau property of Ore extensions

Cited by in corpus (4)

• On the discriminant of twisted tensor products
• Two-generated algebras and standard-form congruence
• Note on Nakayama automorphisms of PBW deformations and Hopf actions
• Skew Calabi-Yau property of normal extensions