Isomorphisms of graded skew Clifford algebras

Chandler, Richard G.; Engel, Nicholas

doi:10.2140/involve.2020.13.871

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Isomorphisms of graded skew Clifford algebras

Richard G. Chandler and Nicholas Engel

Vol. 13 (2020), No. 5, 871–878

DOI: 10.2140/involve.2020.13.871

Abstract

A regular algebra of global dimension $n + 1$ is often called a quantum $ℙ^{n}$ . In 2011, Nafari, Vancliff and Zhang showed that graded skew Clifford algebras (GSCAs) could be used to classify most quadratic quantum $ℙ^{2}$ s. Some time later, Chandler, Tomlin and Vancliff used their work with certain families of GSCAs to develop a conjecture on the quantum space of a generic quadratic quantum $ℙ^{3}$ . These results suggest that (the isomorphism classes of) GSCAs are likely to play a fundamental role in the classification of quadratic quantum $ℙ^{3}$ s. In this article, we will discuss some of these results on GSCAs and discuss new results on isomorphisms between GSCAs.

Keywords

graded skew Clifford algebras, $\mu$-symmetry, isomorphisms

Mathematical Subject Classification

Primary: 16S37, 16S38

Milestones

Received: 22 June 2020

Revised: 7 August 2020

Accepted: 10 August 2020

Published: 5 December 2020

Communicated by Vadim Ponomarenko

Authors

Richard G. Chandler
Department of Mathematics and Information Sciences University of North Texas at Dallas Dallas, TX United States

Nicholas Engel
Department of Mathematics University of Texas at Arlington Arlington, TX United States

Vol. 13, No. 5, 2020