The Cayley–Dickson process for dialgebras

Raúl Felipe-Sosa, Raúl Felipe, Juana Sánchez-Ortega, Murray R. Bremner, Michael K. Kinyon
2013 Linear and multilinear algebra  
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.
doi:10.1080/03081087.2013.791817 fatcat:2blldkxfanhtzm45i6j2u6hjdm