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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.
17A35 Nonassociative division algebras
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17A60 Structure theory for nonassociative algebras
Full Text: DOI
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