More properties of Yetter-Drinfeld category over dual quasi-Hopf algebras

Let \(H\) be a dual quasi-Hopf algebra. In this paper we will firstly introduce all possible categories of Yetter-Drinfeld modules over \(H\), and give explicitly the monoidal and braided structure of them. Then we prove that the category \(^H_H\mathcal{YD}^{fd}\) of finite-dimensional left-left Yet...

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Published in:arXiv.org 2020-10
Main Authors: Lu, Daowei, Zhang, Xiaohui, Wang, Dingguo
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description Let \(H\) be a dual quasi-Hopf algebra. In this paper we will firstly introduce all possible categories of Yetter-Drinfeld modules over \(H\), and give explicitly the monoidal and braided structure of them. Then we prove that the category \(^H_H\mathcal{YD}^{fd}\) of finite-dimensional left-left Yetter-Drinfeld modules is rigid. Finally we will study the braided cocommunitivity of \(H_0\) in \(^H_H\mathcal{YD}\).
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Modules
title More properties of Yetter-Drinfeld category over dual quasi-Hopf algebras
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