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arXiv · 1209.2645

The Cayley-Dickson process for dialgebras

R. Felipe-Sosa·R. Felipe·J. Sanchez-Ortega·M. R. Bremner·M. K. Kinyon
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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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R. Felipe-Sosa, R. Felipe, J. Sanchez-Ortega, M. R. Bremner, M. K. Kinyon. 2012-09-12. The Cayley-Dickson process for dialgebras. https://arxiv.org/abs/1209.2645

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