Graded sets, graded groups, and Clifford algebras

Abstract

We define a general notion of centrally $\Gamma$-graded sets and groups and of their graded products, and prove some basic results about the corresponding categories: most importantly, they form braided monoidal categories. Here, $\Gamma$ is an arbitrary (generalized) ring. The case $\Gamma$ = Z/2Z is studied in detail: it is related to Clifford algebras and their discrete Clifford groups (also called Salingaros Vee groups).

References in corpus (3)

• Clifford algebra, geometric algebra, and applications
• A Categorical Formulation of Superalgebra and Supergeometry
• On Clifford Algebras and Related Finite Groups and Group Algebras