2024/03/19 by Daniele Corradetti, Corradetti, Daniele
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2403.12569
openalex publication_date 2024/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalized Hurwitz theorem states that there are fifteen composition algebras for any given field: seven unital, six para-unital, and two non-unital algebras. In this article we explore the recovery of such algebras from 3D Geometric Algebras. Different involutions, such as reversion, inversion, Clifford conjugation, and full grade inversion, are introduced in order to recover the norm of all composition algebras. A special attention is given to composition algebras of dimension 8, i. e. octonions, para-octonions and Okubo algebra, for which the introduction of a different product is needed.