On Clifford Algebras and Related Finite Groups and Group Algebras

2016/10/12 by Rafał Abłamowicz, Ablamowicz, Rafal
Mathematics · #15A66 #16S35 #20B05 #20C05 #68W30 (Primary) #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1610.03583

openalex publication_date 2016/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Albuquerque and Majid have shown how to view Clifford algebras \cl_p,q as twisted group rings whereas Chernov has observed that Clifford algebras can be viewed as images of group algebras of certain 2-groups modulo an ideal generated by a nontrivial central idempotent. Ablamowicz and Fauser have introduced a special transposition anti-automorphism of \cl_p,q, which they called a "transposition", which reduces to reversion in algebras \cl_p,0 and to conjugation in algebras \cl_0,q. The purpose of this paper is to bring these concepts together in an attempt to investigate how the algebraic properties of real Clifford algebras, including their periodicity of eight, are a direct consequence of the central product structure of Salingaros vee groups viewed as 2-groups.

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