Automorphisms of Twisted Chevalley Groups of type ${}^2 A_3$ and ${}^2 A_4$ over Local Rings

Abstract

This paper is part of an ongoing series devoted to the classification of automorphisms and isomorphisms of twisted Chevalley groups over commutative rings. In our previous work~\cite{EB&DM1}, we established that over local rings containing $1/2$, all automorphisms of twisted Chevalley groups and their elementary subgroups of type ${}^2A_{\ell}$ ($\ell \geq 5$) are standard. In the present paper, we address the remaining low-rank cases and provide a complete classification of the automorphisms of groups of types ${}^2A_3$ and ${}^2A_4$ over local rings $R$ containing $1/2$, across all isogeny types.