On S-Evolution Algebras and Their Enveloping Algebras

Mukhamedov, Farrukh; Qaralleh, Izzat

doi:10.3390/math9111195

Cited by 10 publications

(6 citation statements)

References 46 publications

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“…Recently, in [ 38 , 39 , 40 , 41 ], derivations of Lotka–Volterra algebras have been described. Furthermore, other types of genetic algebras have been investigated in [ 42 , 43 , 44 , 45 , 46 , 47 ].…”

Section: Introductionmentioning

confidence: 99%

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Mukhamedov,

Qaralleh,

Qaisar

et al. 2023

Entropy

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The present paper deals with a class of ξ(a)-quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with ξ(a)-QSOs. Namely, the associativity, characters and derivations of genetic algebras are studied. Moreover, the dynamics of these operators are also explored. Specifically, we focus on a particular partition that results in nine classes, which are further reduced to three nonconjugate classes. Each class gives rise to a genetic algebra denoted as Ai, and it is shown that these algebras are isomorphic. The investigation then delves into analyzing various algebraic properties within these genetic algebras, such as associativity, characters, and derivations. The conditions for associativity and character behavior are provided. Furthermore, a comprehensive analysis of the dynamic behavior of these operators is conducted.

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Section: Introductionmentioning

confidence: 99%

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Mukhamedov,

Qaralleh,

Qaisar

et al. 2023

Entropy

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“…Therefore, in [34], the exploration of Volterra evolution algebras was initiated; these are related to genetic Volterra algebras [35]. Furthermore, in [36], we studied S-evolution algebras which are more general than Volterra ones. In the mentioned paper, solvability, simplicity, semisimlicity, and the structure of enveloping algebras using the attached graph were carried out.…”

Section: Introductionmentioning

confidence: 99%

On Extendibility of Evolution Subalgebras Generated by Idempotents

Mukhamedov

Qaralleh

2023

Mathematics

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In the present paper, we examined the extendibility of evolution subalgebras generated by idempotents of evolution algebras. The extendibility of the isomorphism of such subalgebras to the entire algebra was investigated. Moreover, the existence of an evolution algebra generated by arbitrary idempotents was also studied. Furthermore, we described the tensor product of algebras generated by arbitrary idempotents and found the conditions of the tensor decomposability of four-dimensional S-evolution algebras. This paper’s findings shed light on the field of algebraic structures, particularly in studying evolution algebras. By examining the extendibility of evolution subalgebras generated by idempotents, we provide insights into the structural properties and relationships within these algebras. Understanding the isomorphism of such subalgebras and their extension allows a deeper comprehension of the overall algebraic structure and its behaviour.

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“…On the other hand, recently, in [27], we introduced a new class of evolution algebras called S-evolution algebras. These algebras are not nilpotent and naturally extended Lotka-Volterra evolution algebras [18].…”

Section: Introductionmentioning

confidence: 99%

Entropy Treatment of Evolution Algebras

Mukhamedov

Qaralleh

2022

Entropy

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In this paper, by introducing an entropy of Markov evolution algebras, we treat the isomorphism of S-evolution algebras. A family of Markov evolution algebras is defined through the Hadamard product of structural matrices of non-negative real S-evolution algebras, and their isomorphism is studied by means of their entropy. Furthermore, the isomorphism of S-evolution algebras is treated using the concept of relative entropy.

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On S-Evolution Algebras and Their Enveloping Algebras

Cited by 10 publications

References 46 publications

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

On Extendibility of Evolution Subalgebras Generated by Idempotents

Entropy Treatment of Evolution Algebras

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