Properties of Nilpotent Evolution Algebras with no Maximal Nilindex

Authors

  • Ahmad Alarfeen
  • Izzat Qaralleh
  • Azhana Ahmad

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3912

Keywords:

evolution algebra, derivation, local derivation, automorphism, local automorphism.

Abstract

As a system of abstract algebra, evolution algebras are commutative and non-associative algebras. There is no deep structure theorem for general non-associative algebras. However, there are deep structure theorem and classification theorem for evolution algebras because it has been introduced concepts of dynamical systems to evolution algebras. Recently, in [25], it has been studied some properties of nilpotent evolution algebra with maximal index (dim E2 = dim E − 1). This paper is devoted to studying nilpotent finite-dimensional evolution algebras E with dim E2 =dim E − 2. We describe Lie algebras related to the evolution of algebras. Moreover, this result allowed us to characterize all local and 2-local derivations of the considered evolution algebras. All automorphisms and local automorphisms of the nilpotent evolution algebras are found.

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Published

2021-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Properties of Nilpotent Evolution Algebras with no Maximal Nilindex. (2021). European Journal of Pure and Applied Mathematics, 14(1), 278-300. https://doi.org/10.29020/nybg.ejpam.v14i1.3912