Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex

TL;DR

This paper characterizes the automorphisms, derivations, and Lie algebra structures of finite-dimensional nilpotent evolution algebras with maximal nilindex, providing a comprehensive understanding of their algebraic properties.

Contribution

It fully describes the automorphisms, derivations, and associated Lie algebras of nilpotent evolution algebras with maximal nilindex, a novel classification in this area.

Findings

Complete characterization of automorphisms and local automorphisms.

Explicit description of derivations and 2-local derivations.

Construction of nilpotent evolution algebras with maximal nilindex.

Abstract

In this paper is devoted to nilpotent finite-dimensional evolution algebras E with $dimE^2 = dimE-1$. 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.