Geodesic
Division algebras that generalize Dickson semifields
Communications in Mathematics, Tome 28 (2020) no. 2, pp. 89-102

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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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     author = {Thompson, Daniel},
     title = {Division algebras that generalize {Dickson} semifields},
     journal = {Communications in Mathematics},
     pages = {89--102},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2020},
     mrnumber = {4162923},
     zbl = {07300183},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2020__28_2_a0/}
}
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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/