The evolution operator of evolution algebras

Fernández-Ternero, Desamparados; Gómez-Sousa, Víctor M.; Valdés, Juan Núñez

doi:10.1080/03081087.2021.1878998

Cited by 3 publications

(12 citation statements)

References 8 publications

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“…In this section, we study those evolution algebras over C such that L ∈ Der(E), i.e., the evolution operator is a derivation. This condition, as shown in [21], is equivalent to…”

Section: Evolution Algebras Whose Evolution Operator Is a Derivationmentioning

confidence: 99%

“…In [21], a study is carried out to characterize these types of algebras, up to ordering of the basis elements, reaching the following results.…”

Section: Evolution Algebras Whose Evolution Operator Is a Derivationmentioning

confidence: 99%

“…Additionally, the complete classification for dimensions less than five is given in [21]. We will focus on the classification for larger dimensions, and we will give a result that allows us to characterize the non-degenerate case without using the previous algorithm.…”

Section: Stepmentioning

confidence: 99%

“…For the degenerate cases, we use the previous algorithm. The complete classification in dimension 4 is the following (see [21]):…”

Section: Five-dimensional Evolution Algebrasmentioning

confidence: 99%

“…In Section 2, we briefly introduce the main definitions and properties of evolution algebras. In Section 3, we review the main results obtained in [21], and we develop the methods outlined in this paper in order to extend the classification of these algebras to any dimension through a characterization theorem. Finally, we present some applications of this type of evolution algebras in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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Using the Evolution Operator to Classify Evolution Algebras

Fernández-Ternero¹,

Gómez-Sousa²,

Valdés³

2021

MCA

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Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A criterion for classifying those satisfying certain conditions is given and an algorithm to obtain degenerate evolution algebras starting from those of smaller dimensions is also analyzed and constructed.

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“…In this section, we study those evolution algebras over C such that L ∈ Der(E), i.e., the evolution operator is a derivation. This condition, as shown in [21], is equivalent to…”

Section: Evolution Algebras Whose Evolution Operator Is a Derivationmentioning

confidence: 99%

“…In [21], a study is carried out to characterize these types of algebras, up to ordering of the basis elements, reaching the following results.…”

Section: Evolution Algebras Whose Evolution Operator Is a Derivationmentioning

confidence: 99%

Section: Stepmentioning

confidence: 99%

“…For the degenerate cases, we use the previous algorithm. The complete classification in dimension 4 is the following (see [21]):…”

Section: Five-dimensional Evolution Algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Using the Evolution Operator to Classify Evolution Algebras

Fernández-Ternero¹,

Gómez-Sousa²,

Valdés³

2021

MCA

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Evolution algebras whose evolution operator is a homomorphism

Fernández-Ternero

Gómez-Sousa

Valdés

2021

Comp and Math Methods

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This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n−2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.

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On S-Evolution Algebras and Their Enveloping Algebras

Mukhamedov

Qaralleh

2021

Mathematics

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In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of S-evolution algebras, and prove such derivations can be extended to their enveloping algebras under certain conditions.

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The evolution operator of evolution algebras

Cited by 3 publications

References 8 publications

Using the Evolution Operator to Classify Evolution Algebras

Using the Evolution Operator to Classify Evolution Algebras

Evolution algebras whose evolution operator is a homomorphism

On S-Evolution Algebras and Their Enveloping Algebras

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