Division algebras that generalize Dickson semifields

Daniel Thompson

We generalize Knuth's construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension 2s 2 by doubling central division algebras of degree s. Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

Domaines: Mathématiques [math]

Daniel Thompson. Division algebras that generalize Dickson semifields. Communications in Mathematics, 2020, Volume 28 (2020), Issue 2 (Special Issue: 2nd International Workshop on Nonassociative Algebras in Porto) (2), pp.89 - 102. ⟨10.2478/cm-2020-0012⟩. ⟨hal-03664994⟩