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arXiv · 1906.01329

Division algebras that generalize Dickson semifields

Daniel Thompson
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Abstract

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.

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Daniel Thompson. 2019-06-04. Division algebras that generalize Dickson semifields. https://arxiv.org/abs/1906.01329

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