Another construction of the braided T-category

Yang, Tao; Zhou, Xiaoyan

doi:10.1142/s0219498817500359

Cited by 2 publications

(1 citation statement)

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“…For this, Panaite and Staic [10] gave some interesting constructions in the case of Hopf algebra. Motivated by this, Yang [19], [20], Liu [4] and You [21] generalized their work to multiplier Hopf algebra, weak Hopf algebra and monoidal Hom-Hopf algebra cases, also the authors obtain some new classes of braided crossed categories which provided some solutions to the quantum Yang-Baxter equation over π.…”

Section: Introductionmentioning

confidence: 96%

Drinfel’d construction for Hom–Hopf T-coalgebras

Yan

Wang

2020

Int. J. Math.

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Let [Formula: see text] be a Hom–Hopf T-coalgebra over a group [Formula: see text] (i.e. a crossed Hom–Hopf [Formula: see text]-coalgebra). First, we introduce and study the left–right [Formula: see text]-Yetter–Drinfel’d category [Formula: see text] over [Formula: see text], with [Formula: see text], and construct a class of new braided T-categories. Then, we prove that a Yetter–Drinfel’d module category [Formula: see text] is a full subcategory of the center [Formula: see text] of the category of representations of [Formula: see text]. Next, we define the quasi-triangular structure of [Formula: see text] and show that the representation crossed category [Formula: see text] is quasi-braided. Finally, the Drinfel’d construction [Formula: see text] of [Formula: see text] is constructed, and an equivalent relation between [Formula: see text] and the representation of [Formula: see text] is given.

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