Isomorphism Classes and Automorphisms of Locally Complex Algebras

Locally complex algebras, introduced by M. Bresar, P. Šemrl, and Š. Špenko, 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 specific 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. Bibliography: 5 titles. © 2014 Springer Science+Business Media New York.