The Cayley-Dickson process for dialgebras
  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. 
R. Felipe-Sosa, R. Felipe, J. Sanchez-Ortega, M. R. Bremner, M. K.   Kinyon
math.RA