Classifying Quadratic Quantum P^2s by using Graded Skew Clifford Algebras
Rings and Algebras
2017-05-31 v2
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.
Cite
@article{arxiv.1011.5279,
title = {Classifying Quadratic Quantum P^2s by using Graded Skew Clifford Algebras},
author = {Manizheh Nafari and Michaela Vancliff and Jun Zhang},
journal= {arXiv preprint arXiv:1011.5279},
year = {2017}
}