CLIFFORD ALGEBRA PERIODICITY FOR CENTRAL SIMPLE ALGEBRAS WITH AN INVOLUTION

Abstract

An n-fold orthogonal sum for central simple algebras with an involution is defined, and periodicity is obtained for the associated Clifford algebra when the involution is orthogonal.

Keywords:

• Algebras with involution
• Clifford algebras
• Periodicity

ACKNOWLEDGMENTS

I thank my advisor, David W. Lewis, for suggesting the topic of this paper and for his guidance. I also thank Kevin Hutchinson for showing me how my original definition of semi-Brauer equivalence could be improved and used to construct the Brauer ring. Finally I thank the referee for his helpful suggestions.

This research is supported by Enterprise Ireland.