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Graded sets, graded groups, and Clifford algebras

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arxiv 2109.00878 v1 pith:LVL7TQJR submitted 2021-09-02 math.CT math.GR

Wolfgang Bertram (IECL) This is my paper · ORCID
classification math.CTmath.GR
keywords gradedgroupscliffordgammaalgebrascategoriessetsarbitrary
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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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  1. On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory

    math.LO 2025-01 conditional novelty 3.0 of 10

    Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.

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