Derivations of evolution algebras associated to graphs over a field of any characteristic

Reis, Tiago; Cadavid, Paula

doi:10.1080/03081087.2020.1818673

Cited by 14 publications

(14 citation statements)

References 18 publications

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“…Examples of usual topics in the literature, which have proven to be a very convenient approach, are the study of derivation spaces [11][12][13][14][15] and the classification of some family of evolution algebras sharing interesting properties. For example, nilpotent evolution algebras are characterized in [16][17][18] and power-associative evolution algebras are classified in [19], up to dimension six.…”

Section: Introductionmentioning

confidence: 99%

A Characterization of Associative Evolution Algebras

Fernández-Ternero

Gómez-Sousa²,

Valdés³

2023

Contemp. Math.

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Evolution algebras are non-associative in general, that is, the binary multiplication law is not associative. However, there exist some of them that are associative. In this paper we deal with these last ones. We give an explicit classification of these algebras and show that the concept of associativity is equivalent to the existence of an unitary element for non-degenerate evolution algebras. We also explicitly describe the derivation space of these algebras.

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Section: Introductionmentioning

confidence: 99%

A Characterization of Associative Evolution Algebras

Fernández-Ternero

Gómez-Sousa²,

Valdés³

2023

Contemp. Math.

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“…A few papers are devoted to non-nilpotent evolution algebras [25][26][27]. In [28][29][30], a new class of evolution algebras called Lotka-Volterra evolution algebras has been introduced (see also [31]). An algebra is said to be nilpotent if there exists a natural integer m such that any product of m elements of the algebra is zero.…”

Section: Introductionmentioning

confidence: 99%

“…Later on, evolution algebras are used to model non-Mendelian genetics laws [9][10][11][12][13]. Moreover, these algebras are tightly connected with group theory, the theory of knots, dynamic systems, Markov processes, and graph theory [14][15][16][17][18] and [43,44,46]. Evolution algebras introduced proper algebraic techniques and methods for investigating some digraphs because such algebras and weighted digraphs can be canonically identified [7,19].…”

Section: Introductionmentioning

confidence: 99%

Tensor product of finite dimensional nilpotent evolution algebras

izzat

2022

Preprint

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This paper investigates the tensor product of a finite-dimensional nilpotent evolution algebra. Some properties that translate from tensor products to factors and vice versa have been investigated, including the index of nilpotency and annihilator. The index of nilpotency of the tensor product of two nilpotent evolution algebras with different indexes of nilpotency is determined. Moreover, we investigate the tensorially decomposable of the 4-dimensional nilpotent evolution algebra. In addition, the decomposable nilpotent evolution algebra with the maximal nilindex of nilpotency has been carried out.

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“…Here we mention some of the recent works, and we refer the reader to the references therein for a deeper study of the theory. In [3][4][5][6][7] the reader may find a survey of properties and results of general evolution algebras; the works in [1,2,8,14] are devoted to the connections between evolution algebras and graphs together with some related properties; and in [10,12] one may see a good review of results with relevance in genetics and other applications.…”

Section: Introductionmentioning

confidence: 99%