Twisted Rota-Baxter operators on 3-Hom-Lie algebras

Li, Yizheng; Wang, Dingguo

doi:10.1080/00927872.2023.2215321

Cited by 3 publications

(7 citation statements)

References 17 publications

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“…In this section, we introduce the notion of generalized Reynolds operators on Hom-Lie triple systems, which can be regarded as the generalization of relative Rota-Baxter operators on Hom-Lie triple systems [17,19] and generalized Reynolds operators on Lie triple systems [29,30]. We give its characterization by a graph and provide some examples.…”

Section: Generalized Reynolds Operators On Hom-lie Triple Systemsmentioning

confidence: 99%

“…(ii) Any relative Rota-Baxter operator (in particular, a Rota-Baxter operator of weight 0) on a Hom-Lie triple system is a generalized Reynolds operator with H = 0. See [17,19] for more details about relative Rota-Baxter operators on Hom-Lie triple systems.…”

Section: Generalized Reynolds Operators On Hom-lie Triple Systemsmentioning

confidence: 99%

“…Subsequently, the notion of a relative Rota-Baxter operator (also called an O-operator) on a Lie algebra was independently introduced by Kupershmidt [13], to better understand the classical Yang-Baxter equation and related integrable systems. Recently, relative Rota-Baxter operators have been widely studied (see [14][15][16][17][18][19]). In addition, other operators related to (relative) Rota-Baxter operators are constantly emerging.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Reynolds Operators on Hom-Lie Triple Systems

Xiao,

Teng,

Long

2024

Preprint

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Uchino first initiated the study of generalized Reynolds operators on associative algebras. Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

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Section: Generalized Reynolds Operators On Hom-lie Triple Systemsmentioning

confidence: 99%

Section: Generalized Reynolds Operators On Hom-lie Triple Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Reynolds Operators on Hom-Lie Triple Systems

Xiao,

Teng,

Long

2024

Preprint

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Section: Introductionmentioning

confidence: 99%

“…Das also developed the notions of generalized Reynolds operators on Lie algebras and NS-Lie algebras in [24]. Generalized Reynolds operators on other algebraic structures have also been widely studied, including 3-Lie algebras [25,26], 3-Hom-Lie algebras [27], Hom-Lie algebras [28], Lie-Yamaguti algebras [29], Lie triple systems [29,30] and Lie supertriple systems [31].…”

Section: Introductionmentioning

confidence: 99%

Generalized Reynolds Operators on Hom-Lie Triple Systems

Xiao,

Teng,

Long

2024

Symmetry

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In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop a cohomology of generalized Reynolds operators on Hom-Lie triple systems. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order n deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

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Twisted Rota-Baxter operators on Hom-Lie algebras

Xu,

Wang,

Zhao

2023

MATH

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<abstract><p>Uchino initiated the investigation of twisted Rota-Baxter operators on associative algebras. Relevant studies have been extensive in recent times. In this paper, we introduce the notion of a twisted Rota-Baxter operator on a Hom-Lie algebra. By utilizing higher derived brackets, we establish an explicit $ L_{\infty} $-algebra whose Maurer-Cartan elements are precisely twisted Rota-Baxter operators on Hom-Lie algebra s. Additionally, we employ Getzler's technique of twisting $ L_\infty $-algebras to establish the cohomology of twisted Rota-Baxter operators. We demonstrate that this cohomology can be regarded as the Chevalley-Eilenberg cohomology of a specific Hom-Lie algebra with coefficients in an appropriate representation. Finally, we study the linear and formal deformations of twisted Rota-Baxter operators by using the cohomology defined above. We also show that the rigidity of a twisted Rota-Baxter operator can be derived from Nijenhuis elements associated with a Hom-Lie algebra.</p></abstract>

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Twisted Rota-Baxter operators on 3-Hom-Lie algebras

Cited by 3 publications

References 17 publications

Generalized Reynolds Operators on Hom-Lie Triple Systems

Generalized Reynolds Operators on Hom-Lie Triple Systems

Generalized Reynolds Operators on Hom-Lie Triple Systems

Twisted Rota-Baxter operators on Hom-Lie algebras

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