The Cayley-Dickson process for dialgebras

2012/09/12 by R. Felipe-Sosa, Felipe-Sosa, R., R. Felipe +7
Mathematics · #17A30 #17A32 (Primary) 17A20 #17A75 #17C50 #17D05 #17D10 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17A20 #msc:17A30 #msc:17A32 #msc:17A75 #msc:17C50 #msc:17D05 #msc:17D10

paper · pdf · doi:10.48550/arxiv.1209.2645

18 pages

arxiv created 2012/09/12 · arxiv updated 2012/09/13

Abstract

We adapt the algorithm of Kolesnikov and Pozhidaev, which converts a polynomial identity for algebras into the corresponding identities for dialgebras, to the Cayley-Dickson doubling process. We obtain a generalization of this process to the setting of dialgebras, establish some of its basic properties, and construct dialgebra analogues of the quaternions and octonions.

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