Properties of Nilpotent Evolution Algebras with no Maximal Nilindex


  • Ahmad Alarfeen
  • Izzat Qaralleh
  • Azhana Ahmad



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


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.






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.

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