Constructing New Braided $T$-Categories via Weak Monoidal Hom-Hopf Algebras

Wei Wang; Shuanhong Wang; Xiaohui Zhang

Constructing New Braided $T$-Categories via Weak Monoidal Hom-Hopf Algebras

Quantum Algebra 2015-02-27 v1

Authors: Wei Wang , Shuanhong Wang , Xiaohui Zhang

Abstract

In this paper, we define and study weak monoidal Hom-Hopf algebras, which generalize both weak Hopf algebras and monoidal Hom-Hopf algebras. If $H$ is a weak monoidal Hom-Hopf algebra with bijective antipode and let $Aut_{wmHH}(H)$ be the set of all automorphisms of $H$ . Then we introduce a category ${_{H}\mathcal{WMHYD}^{H}}(\alpha,\beta)$ with $\alpha,\beta\in Aut_{wmHH}(H)$ and construct a braided $T$ -category $\mathcal{WMHYD}(H)$ that having all the categories ${_{H}\mathcal{WMHYD}^{H}}(\alpha,\beta)$ as components.

Keywords

weak monoidal Hom-Hopf algebras braided T-categories weak Hopf algebras monoidal Hom-Hopf algebras automorphism groups category construction

Cite

@article{arxiv.1502.07377,
  title  = {Constructing New Braided $T$-Categories via Weak Monoidal Hom-Hopf Algebras},
  author = {Wei Wang and Shuanhong Wang and Xiaohui Zhang},
  journal= {arXiv preprint arXiv:1502.07377},
  year   = {2015}
}

Comments

24 pages. arXiv admin note: substantial text overlap with arXiv:1405.6767

Constructing New Braided $T$-Categories via Weak Monoidal Hom-Hopf Algebras

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