Classifying Quadratic Quantum P^2s by using Graded Skew Clifford Algebras

Abstract

We prove that quadratic regular algebras of global dimension three on degree-one generators are related to graded skew Clifford algebras. In particular, we prove that almost all such algebras may be constructed as a twist of either a regular graded skew Clifford algebra or of an Ore extension of a regular graded skew Clifford algebra of global dimension two. In so doing, we classify all quadratic regular algebras of global dimension three that have point scheme either a nodal cubic curve or a cuspidal cubic curve in P^2.

Cited by in corpus (3)

• Two-generated algebras and standard-form congruence
• PBW deformations of Artin-Schelter regular algebras
• On the Notion of Complete Intersection outside the Setting of Skew Polynomial Rings