Classification of the algebras \mathbbO_p,q

2013/12/13 by Marie Kreusch, Kreusch, Marie, Sophie Morier-Genoud +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.AC #math.RA

paper · pdf · doi:10.48550/arxiv.1312.3935

15 pages, 2 figures

arxiv created 2013/12/13 · openalex publication_date 2013/12/13 · arxiv updated 2013/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a series of real nonassociative algebras \mathbbO_p,q introduced in [5]. These algebras have a natural ℤ₂ⁿ-grading, where n=p+q, and they are characterized by a cubic form over the field ℤ₂. We establish all the possible isomorphisms between the algebras \mathbbO_p,q preserving the structure of ℤ₂ⁿ-graded algebra. The classification table of \mathbbO_p,q is quite similar to that of the real Clifford algebras Cl_p,q, the main difference is that the algebras \mathbbO_n,0 and \mathbbO_0,n are exceptional.

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