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Original Articles

Graded Skew Clifford Algebras That Are Twists of Graded Clifford Algebras

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Pages 719-725 | Received 23 Dec 2012, Published online: 22 Oct 2014
 

Abstract

In 2010, a quantized analog of a graded Clifford algebra (GCA), called a graded skew Clifford algebra (GSCA), was proposed by Cassidy and Vancliff, and many properties of GCAs were found to have counterparts for GSCAs. In particular, a GCA is a finite module over a certain commutative subalgebra C, while a GSCA is a finite module over a (typically noncommutative) analogous subalgebra R. We consider the case that a regular GSCA is a twist of a GCA by an automorphism, and we prove, in this case, R is a skew polynomial ring and a twist of C by an automorphism.

2010 Mathematics Subject Classification:

ACKNOWLEDGMENT

The authors thank S. P. Smith of the University of Washington for the suggestion to study the subalgebra R.

Notes

Communicated by E. Kirkman.

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