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Division algebras that generalize Dickson semifields. (English) Zbl 07300183
Summary: 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.
MSC:
17A35 Nonassociative division algebras
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17A60 Structure theory for nonassociative algebras
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