A generalization of Dickson’s commutative division algebras

Abstract

Dickson’s commutative semifields are an important class of finite division algebras. We generalize Dickson’s construction over any base field by doubling not just finite field extensions (which would correspond to the classical setup), but also central simple algebras. The latter case yields division algebras which are no longer commutative nor associative. We compute their automorphisms.

Keywords:

• Automorphisms
• division algebras
• nonassociative algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 17A35
• Secondary: 17A36
• 17A60