Cayley Polynomials

2006/01/23 by Yōji Yoshii, Yoji Yoshii, Yoshii, Yoji · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematics and Applications #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.math/0601570

arxiv created 2006/01/23 · openalex publication_date 2006/01/23 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We consider a polynomial version of the Cayley numbers. Namely, we define the ring of Cayley polynomials in terms of generators and relations in the category of alternative algebras. The ring turns out to be an octonion algebra over an ordinary polynomial ring. Also, a localization (a ring of quotients) of the ring of Cayley polynomials gives another description of an octonion torus. Finally, we find a subalgebra of a prime nondegenerate alternative algebra so that the subalgebra is an octonion algebra over the center.

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