GRADED SKEW CLIFFORD ALGEBRAS THAT ARE TWISTS OF GRADED CLIFFORD ALGEBRAS

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.