ABSTRACT
A division algebra is an algebra where the left and right multiplication operators LX, RX by any nonzero element x are bijective. This chapter deals with the development of a program for division composition algebras over arbitrary fields of characteristic φ 2 or 3. It computes the derivation algebra of these algebras, obtaining an analogous of Theorem 1. We deal with the description and classification of these algebras. Two Hurwitz algebras are isomorphic if and only if their quadratic forms are equivalent. In case this form has nonzero isotropic vectors, then the Witt index is maximum; therefore, Hurwitz algebras of the same dimension with nonzero isotropic vectors are isomorphic.
