Novikov Commutator Algebras are Special

Kolesnikov, Pavel; Panasenko, A. S.

doi:10.1007/s10469-020-09571-2

Cited by 4 publications

(8 citation statements)

References 3 publications

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“…As a result of the same computations as for n = 4, we obtain three special identities of degree 5: (16) and…”

Section: Special Identities Of Gd-algebrasmentioning

confidence: 70%

“…Therefore, the structure of a GD-algebra on V is almost completely similar to the commutator GD-algebra on a Novikov algebra considered in [16]. The only difference is the multiplicative constant 1 γ−α which does not affect the construction of a differential Poisson envelope.…”

Section: Special Gd-algerbasmentioning

confidence: 85%

“…Then apply the Leibniz rule to expand the bracket on the entire F . The bracket obtained is proportional to the one considered in [16]. Therefore, the operation (4) satisfies the Jacobi identity, and the operation d is a derivation with respect to this bracket.…”

Section: Special Gd-algerbasmentioning

confidence: 98%

“…The examples of non-special GD-algebras were constructed in [10], [16]. It is worth mentioning that all these examples are of dimension 3.…”

Section: Special Gd-algerbasmentioning

confidence: 99%

“…Non-special GD-algebras exist: the examples were found implicitly in [10] and explicitly in [16]. Note that all these examples are of dimension three.…”

mentioning

confidence: 99%

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On the special identities of Gelfand--Dorfman algebras

Kolesnikov¹,

Sartayev²

2021

Preprint

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In this paper, we prove that the class of all special Gelfand-Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that every 2-dimensional GD-algebra is special. For the latter, we give a technical method to find all special identities of GD-algebras and compute the degree 6 component of the Gröbner basis for the shuffle operad constructed on the symmetric operad governing the class of GD-algebras.

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“…As a result of the same computations as for n = 4, we obtain three special identities of degree 5: (16) and…”

Section: Special Identities Of Gd-algebrasmentioning

confidence: 70%

Section: Special Gd-algerbasmentioning

confidence: 85%

Section: Special Gd-algerbasmentioning

confidence: 98%

“…The examples of non-special GD-algebras were constructed in [10], [16]. It is worth mentioning that all these examples are of dimension 3.…”

Section: Special Gd-algerbasmentioning

confidence: 99%

“…Non-special GD-algebras exist: the examples were found implicitly in [10] and explicitly in [16]. Note that all these examples are of dimension three.…”

mentioning

confidence: 99%

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On the special identities of Gelfand--Dorfman algebras

Kolesnikov¹,

Sartayev²

2021

Preprint

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On the Special Identities of Gelfand–Dorfman Algebras

Kolesnikov

Sartayev

2022

Experimental Mathematics

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Hom-pre-Poisson superalgebras and Dual Hom-pre-Poisson superalgebras

Aloulou

2024

Preprint

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In this research paper, we investigate the concept of Hom-superalgebras obtained by an internal law defined on ℤ2-graded vector space A equipped with an algebra morphism f. Given a structure of Hom-pre-Lie superalgebra (A,◊,f) and Hom-Zinbiel superalgebras (A,Λ,f), we define the structure of Hom-pre-Poisson superalgebras (A,◊,Λ,f) verifying two compatibility conditions between ”◊” and ”Λ”. On the one hand, we demonstrate that when A is a Hom-pre-Lie superalgebra, then a tensoriel algebra of A has a structure of Hom-pre-Poisson superalgebra. On the other hand, we prove that any Hom-Poisson superalgebra equipped with a Baxter operator can define a structure of Hom-pre-Poisson superalgebra. Furthermore, we combine a structure of Hompermutative superalgebra and Hom-Leibniz superalgebra on the same space, we define a structure of dual Hom-pre-Poisson superalgebra and we reveal that any Hom-Poisson superalgebra equipped with an Averaging operator can define a structure of dual Hom-pre-Poisson superalgebra. (MSC) : 17A60, 17A30, 17D30, 17B63, 17A36.

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Novikov Commutator Algebras are Special

Cited by 4 publications

References 3 publications

On the special identities of Gelfand--Dorfman algebras

On the special identities of Gelfand--Dorfman algebras

On the Special Identities of Gelfand–Dorfman Algebras

Hom-pre-Poisson superalgebras and Dual Hom-pre-Poisson superalgebras

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