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

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

2010-11-24

arxiv.org/abs/1011.5279v2

Mathematics

Rings and Algebras

Scientific paper

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.

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