Daniel Thompson
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Division algebras that generalize Dickson semifields
cm:9504 -
Communications in Mathematics,
October 11, 2020,
Volume 28 (2020), Issue 2 (Special Issue: 2nd International Workshop on Nonassociative Algebras in Porto)
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https://doi.org/10.2478/cm-2020-0012
Division algebras that generalize Dickson semifieldsArticle
Authors: Daniel Thompson
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Daniel Thompson
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.