On unified Hom–Yetter–Drinfeld categories

Ma, Tianshui; Yang, Haiyan; Liu, Linlin; Chen, Quanguo

doi:10.1016/j.geomphys.2019.05.015

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Cited by 10 publications

(2 citation statements)

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“…In [29,31] Yau proposed the definition of quasitriangular Hom-Hopf algebras and showed that each quasitriangular Hom-Hopf algebra yields a solution of the Hom-Yang-Baxter equation. Meanwhile, several classes of solutions of the Hom-Yang-Baxter equation were constructed from different respects, including those associated to Hom-Lie algebras [5,25,29,30], Drinfeld (co)doubles [2,34,35] and Hom-Yetter-Drinfeld modules [3,10,13,14,18,26,33].…”

Section: Introductionmentioning

confidence: 99%

Hom-Yang-Baxter equations and Hom-Yang-Baxter systems

Wang¹,

Zhang²,

Guo³

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Hom-Yang-Baxter equations and Hom-Yang-Baxter systems

Wang¹,

Zhang²,

Guo³

2021

Preprint

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“…The Hom-Yang-Baxter equation reduces to the usual Yang-Baxter equation when the twist map is trivial. Several classes of solutions of the Hom-Yang-Baxter equation were constructed from different respects, including those associated to Hom-Lie algebras [6,28,31,32], Drinfelds (co)doubles [3,37,38], and Hom-Yetter-Drinfeld modules [4,13,17,18,22,29,34].…”

Section: Introductionmentioning

confidence: 99%

The Hom-Long dimodule category and nonlinear equations

Wang¹,

Zhang²,

Guo³

2020

Preprint

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In this paper, we construct a kind of new braided monoidal category over two Hom-Hopf algerbas (H, α) and (B, β) and associate it with two nonlinear equations. We first introduce the notion of an (H, B)-Hom-Long dimodule and show that the Hom-Long dimodule category B H L is an autonomous category. Second, we prove that the category B H L is a braided monoidal category if (H, α) is quasitriangular and (B, β) is coquasitriangular and get a solution of the quantum Yang-Baxter equation. Also, we show that the category B H L can be viewed as a subcategory of the Hom-Yetter-Drinfeld category H⊗B H⊗B HYD. Finally, we obtain a solution of the Hom-Long equation from the Hom-Long dimodules.

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Drinfeld Double for Infinitesimal BiHom-bialgebras

Yang

2020

Adv. Appl. Clifford Algebras

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On unified Hom–Yetter–Drinfeld categories

Cited by 10 publications

References 43 publications

Hom-Yang-Baxter equations and Hom-Yang-Baxter systems

Hom-Yang-Baxter equations and Hom-Yang-Baxter systems

The Hom-Long dimodule category and nonlinear equations

Drinfeld Double for Infinitesimal BiHom-bialgebras

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