Genetic Volterra algebras and their derivations

Ganikhodzhaev, Rasul; Mukhamedov, Farrukh; Pirnapasov, Abror; Qaralleh, Izzat

doi:10.1080/00927872.2017.1347663

Cited by 19 publications

(18 citation statements)

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“…Namely, by looking some properties of Volterra evolution algebras, we could predict dynamical behavior of associated Volterra QSO. We notice that every Volterra QSO defines a genetic algebra (in sense of [20]) whose some properties have been investigated in [13,14]. We point out that our new algebra is not related to these types of algebras.…”

Section: Introductionmentioning

confidence: 97%

Volterra Evolution Algebras and Their Graphs

Qaralleh¹,

Mukhamedov²

2019

Preprint

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In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras with ergodicities of Volterra quadratic stochastic operators. Furthermore, some of properties of the considered algebras such as nilpotency, derivations have been studied as well.

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Section: Introductionmentioning

confidence: 97%

Volterra Evolution Algebras and Their Graphs

Qaralleh¹,

Mukhamedov²

2019

Preprint

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“…The derivation of non-associative algebra forms the Lie algebra, which is considered as one of the important tools for studying its structure. Extensive work has been conducted on the subject of derivations of genetic algebras ( [13], [17], [20], [28], [16], [1]). since the multiplication is trivial then set of all until is invertible In fact, [7,14] have investigated several properties of derivations of n-dimensional complex evolution algebras,depending on the rank of the appropriate matrices.…”

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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“…For any algebra, the space of all its derivations is Lie algebra with respect to the commutator multiplication. In the theory of non-associative algebras, particularly, in genetic algebras, the Lie algebra of derivations of a given algebra is one of the important tools for studying its structure [2,6,7,[11][12][13]. In this regard, the system of equations that describe the derivations of evolution algebras have been posed in [13].…”

Section: Introductionmentioning

confidence: 99%