Yetter-Drinfeld-Long bimodules are modules

Lu, Daowei; Wang, Shuanhong

doi:10.21136/cmj.2017.0666-15

Cited by 3 publications

(3 citation statements)

References 6 publications

(4 reference statements)

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“…is an anti-isomorphism of group. By a similar procedure as in [6], we could obtain this isomorphism.…”

Section: Moreover C Mn Satisfies Relations (11) and (12) And Formentioning

confidence: 91%

“…Suppose H to be a finite dimensional Hopf algebra. In [6] Proof. Let H be a finite dimensional Hopf algebra, then…”

Section: Moreover C Mn Satisfies Relations (11) and (12) And Formentioning

confidence: 99%

“…As we all know, a Hopf algebra in H H YD corresponds to the classic Radford biproduct, while more generally the Hopf algebra in LR(H) corresponds to L-R smash biproduct also defined in [9]. In [6] the first author pointed out that, for H being finite dimensional, LR(H) is actually a Yetter-Drinfeld category.…”

Section: Introductionmentioning

confidence: 99%

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The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules

Lu,

Ning,

Wang

2019

Preprint

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Let H 1 and H 2 be Hopf algebras which are not necessarily finite dimensional and α, β ∈ Aut Hopf (H 1 ), γ, δ ∈ Aut Hopf (H 2 ). In this paper, we introduce a category H 1 LR H 2 (α, β, γ, δ), generalizing Yetter-Drinfeld-Long bimodules and construct a braided T -category LR(H 1 , H 2 ) containing all the categories H 1 LR H 2 (α, β, γ, δ) as components. We also prove that if (α, β, γ, δ) admits a quadruple in involution, then H 1 LR H 2 (α, β, γ, δ) is isomorphic to the usual category H 1 LR H 2 of Yetter-Drinfeld-Long bimodules.

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“…is an anti-isomorphism of group. By a similar procedure as in [6], we could obtain this isomorphism.…”

Section: Moreover C Mn Satisfies Relations (11) and (12) And Formentioning

confidence: 91%

“…Suppose H to be a finite dimensional Hopf algebra. In [6] Proof. Let H be a finite dimensional Hopf algebra, then…”

Section: Moreover C Mn Satisfies Relations (11) and (12) And Formentioning

confidence: 99%

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The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules

Lu,

Ning,

Wang

2019

Preprint

Self Cite

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The Construction of Braided T-Categories via Yetter–Drinfeld–Long Bimodules

Ning

Wang

2021

Appl Categor Struct

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Hom-L-R-smash biproduct and the category of Hom–Yetter–Drinfel’d–Long bimodules

Zhang

2018

J. Algebra Appl.

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Let [Formula: see text] be a Hom-bialgebra. In this paper, we firstly introduce the notion of Hom-L-R smash coproduct [Formula: see text], where [Formula: see text] is a Hom-coalgebra. Then for a Hom-algebra and Hom-coalgebra [Formula: see text], we introduce the notion of Hom-L-R-admissible pair [Formula: see text]. We prove that [Formula: see text] becomes a Hom-bialgebra under Hom-L-R smash product and Hom-L-R smash coproduct. Next, we will introduce a prebraided monoidal category [Formula: see text] of Hom–Yetter–Drinfel’d–Long bimodules and show that Hom-L-R-admissible pair [Formula: see text] actually corresponds to a bialgebra in the category [Formula: see text], when [Formula: see text] and [Formula: see text] are involutions. Finally, we prove that when [Formula: see text] is finite dimensional Hom-Hopf algebra, [Formula: see text] is isomorphic to the Yetter–Drinfel’d category [Formula: see text] as braid monoidal categories where [Formula: see text] is the tensor product Hom–Hopf algebra.

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Yetter-Drinfeld-Long bimodules are modules

Cited by 3 publications

References 6 publications

The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules

The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules

The Construction of Braided T-Categories via Yetter–Drinfeld–Long Bimodules

Hom-L-R-smash biproduct and the category of Hom–Yetter–Drinfel’d–Long bimodules

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