# Division algebras that generalize Dickson semifields

## TL;DR

This paper introduces a new class of division algebras by generalizing Dickson semifields through doubling central simple algebras, expanding the understanding of their structure and symmetries.

## Contribution

It extends Knuth's construction of semifields by doubling central simple algebras, creating new division algebras of specific dimensions.

## Key findings

- Derived conditions for isomorphisms and automorphisms of the new algebras
- Established the structure of these division algebras
- Connected the construction to existing algebraic frameworks

## 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.