The concept of hierarchy of algebras and graphs

Cruz, Francisco J.; Valle, Abraham Del; Valdés, Juan Núñez; Peña, Manuel

doi:10.1007/s12190-020-01493-7

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2023

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“…However, evolution algebras are not associative, in general, which means that some of them are. There is not much information on the latter in the literature, that is the reason for which this article can be considered novel, since it presents a result referring to the associativity of these algebras, which can serve to facilitate the study of more aspects related to this topic in general, and complements the study of other aspects of these algebras that are also rarely discussed, such as hierarchy (see [5]), the fact that they are normed (see [6]), or the links between these algebras and Markov chains (see [7]) or between the same and graphs (see [8][9][10], for instance).…”

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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