A note on 2-local automorphisms of digraph algebras (Q1826718)

Let \(\mathcal A\) be a digraph algebra. If \(\mathcal A\) is symmetric, the authors show that every 2-local automorphism of \(\mathcal A\) is an automorphism. However, when \(\mathcal A\) has not the extra condition of symmetry, the authors produce an example to clarify that the conclusion may not be true. By this means, they give a negative answer to the question whether every 2-local automorphism of a digraph algebra is automatically an automorphism.