Geodesic
Division algebras that generalize Dickson semifields
Communications in Mathematics, Tome 28 (2020) no. 2, pp. 89-102 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 17A35, 17A36, 17A60
Keywords: Nonassociative algebras; division algebras; automorphisms 
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Thompson, Daniel. Division algebras that generalize Dickson semifields. Communications in Mathematics, Tome 28 (2020) no. 2, pp. 89-102. http://geodesic.mathdoc.fr/item/COMIM_2020_28_2_a0/

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