Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex

This paper is devoted to the nilpotent finite-dimensional evolution algebras E with dim E2 =dim E - 1. We describe the Lie algebra of derivations of these algebras. Moreover, in terms of these Lie algebras, we fully construct nilpotent evolution algebra with maximal index of nilpotency. Furthermore, this result allowed us fully characterize all local and 2-local derivations of the considered evolution algebras. Besides, all automorphisms and local automorphisms of these algebras are found.