On Local Automorphisms of ${\mathfrak{sl}}_2$

Abstract

We establish that the set of local automorphisms $\text{LAut}({\mathfrak{sl}}_2)$ is the group ${\text{Aut}}^{\pm }({\mathfrak{sl}}_2)$ of all automorphisms and anti-automorphisms. For $n\ge 3$ we prove that anti-automorphisms are local automorphisms of ${\mathfrak{sl}}_n$.