Note on one family of real division algebras

Abstract

In this paper, we consider a special class of four-dimensional real division algebras called transitive division algebras, and its subclass – transitive-diagonal division algebras. We explicitly describe the automorphism group and the derivation (Lie) algebra of any transitive-diagonal division algebra. Besides, we solve the classification problem for this family of four-dimensional real division algebras.

Keywords:

• Real division algebras
• automorphism groups
• derivation algebras

2010 Mathematics Subject Classifications:

• 17A35
• 17A36

Disclosure statement

No potential conflict of interest was reported by the author(s).