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arXiv · 1912.10654

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

Daowei Lu·Yan Ning·Dingguo Wang
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Abstract

Let $H_1$ and $H_2$ be Hopf algebras which are not necessarily finite dimensional and $\alpha,\beta \in Aut_{Hopf}(H_1), \gamma,\delta \in Aut_{Hopf}(H_2)$. In this paper, we introduce a category ${}_{H_1}\mathcal{LR}_{H_2}(\alpha, \beta, \gamma, \delta)$, generalizing Yetter-Drinfeld-Long bimodules and construct a braided $T$-category $\mathcal{LR}(H_1,H_2)$ containing all the categories $_{H_1}\mathcal{LR}_{H_2}(\alpha, \beta, \gamma, \delta)$ as components. We also prove that if $(\alpha, \beta, \gamma, \delta)$ admits a quadruple in involution, then ${}_{H_1}\mathcal{LR}_{H_2}(\alpha, \beta, \gamma, \delta)$ is isomorphic to the usual category ${}_{H_1}\mathcal{LR}_{H_2}$ of Yetter-Drinfeld-Long bimodules.

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Daowei Lu, Yan Ning, Dingguo Wang. 2019-12-23. The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules. https://arxiv.org/abs/1912.10654

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