On genetic and evolution algebras in dimension three

Mukhamedov, Farrukh; Qaralleh, Izzat; Pirnapasov, Abror

doi:10.12988/ija.2016.6533

Cited by 3 publications

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“…Recently, many paper have been devoted to study the derivation of evolution algebras see for instance [2,26,30,31]. Other properties of evolution algebra have been investigated in [5,6,8,9,11,23,29]. In [25], it has been study the properties of the nilpotent finite-dimensional evolution algebras with maximal nil index such as derivation, local derivation, automorphism, and local automorphism.…”

Section: Introductionmentioning

confidence: 99%

Properties of Nilpotent Evolution Algebras with no Maximal Nilindex

Alarfeen¹,

Qaralleh²,

Ahmad³

2021

Eur. J. Pure Appl. Math.

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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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