Graded Skew Clifford Algebras That Are Twists of Graded Clifford Algebras

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.

Key Words:

• Clifford algebra
• Regular algebra
• Twist
• Quadric

2010 Mathematics Subject Classification:

• 16S38
• 16S37
• 16S36

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.