Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex

Abstract

In this paper is devoted to nilpotent finite-dimensional evolution algebras E with $dim{E}^2=dimE-1$. We described Lie algebras associated with evolution algebras whose nilindex is maximal. Moreover, in terms of this Lie algebra 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. All automorphisms and local automorphisms of the nilpotent evolution algebras with maximal nilindex are found.

23 pages