Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings

Abstract

We study the automorphisms of Jha-Johnson semifields obtained from an invariant irreducible twisted polynomial $f\in K[t;\sigma]$, where $K=\mathbb{F}_{q^n}$ is a finite field and $\sigma$ an automorphism of $K$ of order $n$, with a particualr emphasis on inner automorphisms and the automorphisms of Sandler and Hughes-Kleinfeld semifields. We include the automorphisms of some Knuth semifields (which do not arise from skew polynomial rings). Isomorphism between Jha-Johnson semifields are considered as well.