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Division algebras that generalize Dickson semifields

Daniel Thompson — 2020

Communications in Mathematics

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 $2 s^{2}$ by doubling central division algebras of degree $s$ . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

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