2014
DOI: 10.1142/s0129167x14500128
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Classification Dynamics of Two-Dimensional Chains of Evolution Algebras

Abstract: Recently by Casas et al. a notion of chain of evolution algebras (CEAs) is introduced. This chain is a dynamical system the state of which at each given time is an evolution algebra. It is known 25 distinct classes of chains of two-dimensional evolution algebras. In our previous paper we gave the classification of two-dimensional real evolution algebras. This classification contains seven (pairwise non-isomorphic) such algebras. For each known CEA we study its dynamics to be an element of a given class.

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Cited by 15 publications
(11 citation statements)
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“…On the other hand, chains of evolution algebras (i.e. dynamical systems the state of which at each given time is an evolution algebra) are studied in [5,21,16,17]. Also the derivations of some evolution algebras have been analyzed in [22,3,14].…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, chains of evolution algebras (i.e. dynamical systems the state of which at each given time is an evolution algebra) are studied in [5,21,16,17]. Also the derivations of some evolution algebras have been analyzed in [22,3,14].…”
Section: Introductionmentioning
confidence: 99%
“…The space of derivations of an evolution algebra is a frequent subject of study in the literature [14][15][16][17], although obtaining a complete characterization of this space is still an open question. On the other hand, there are also several studies carried out with the aim of classifying certain evolution algebras [18][19][20]. This paper lives in the intersection of these two subjects.…”
Section: Introductionmentioning
confidence: 99%
“…Both aspects explain the growing interest of researchers in them today. However, only the classification of these algebras up to dimension 3 has been obtained 11‐13 . This article is related to this topic, being the main objective to classify a special family of evolution algebras in dimension 4.…”
Section: Introductionmentioning
confidence: 99%