Graded sets, graded groups, and Clifford algebras

Wolfgang Bertram

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arXiv · 2109.00878

Graded sets, graded groups, and Clifford algebras

Wolfgang Bertram

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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).

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Wolfgang Bertram. 2021-09-02. Graded sets, graded groups, and Clifford algebras. https://arxiv.org/abs/2109.00878

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