On Local Automorphisms of ${\mathfrak{s}\mathfrak{l}}_2$

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