Vol. 13, No. 5, 2020

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Isomorphisms of graded skew Clifford algebras

Richard G. Chandler and Nicholas Engel

Vol. 13 (2020), No. 5, 871–878
Abstract

A regular algebra of global dimension n + 1 is often called a quantum n . In 2011, Nafari, Vancliff and Zhang showed that graded skew Clifford algebras (GSCAs) could be used to classify most quadratic quantum 2s. 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 3 . These results suggest that (the isomorphism classes of) GSCAs are likely to play a fundamental role in the classification of quadratic quantum 3s. 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