Generalizing Classical Clifford Algebras, Graded Clifford Algebras and their Associated Geometry.

This article is based on a talk given by the author at the 12th International Conference on Clifford Algebras and their Applications in Mathematical Physics. A generalization, introduced by Cassidy and the author, of a classical Clifford algebra is discussed together with connections between that generalization and a generalization of a graded Clifford algebra. A geometric approach to studying the algebras, viewed through the lens of Artin, Tate and Van den Bergh’s noncommutative algebraic geometry, is also presented. [ABSTRACT FROM AUTHOR]