Isomorphism classes and automorphisms of locally-complex algebras

Locally-complex algebras, introduced by M. Bresar, P. S̆emrl, and S̆. S̆penko, provide a generalization of Cayley–Dickson algebras to the case of arbitrary dimensions. The paper considers the isomorphic classes of locally-complex algebras and their automorphism groups. As a characterization of the isomorphism classes, a system of cpecific matrix equations is used. This system allows one to derive a few necessary conditions for locally-complex algebras to be isomorphic. Also classifications of locally-complex algebras of dimension three and of their automorphism groups are presented.