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

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 $Au{t}_{wmHH}(H)$ be the set of all automorphisms of $H$. Then we introduce a category ${}_H{\mathcal{W}\mathcal{M}\mathcal{H}\mathcal{YD}}^H(\hat{I}\pm ,{\hat{I}}^2)$ with $\hat{I}\pm ,{\hat{I}}^2\in Au{t}_{wmHH}(H)$ and construct a braided $T$-category $\mathcal{W}\mathcal{M}\mathcal{H}\mathcal{YD}(H)$ that having all the categories ${}_H{\mathcal{W}\mathcal{M}\mathcal{H}\mathcal{YD}}^H(\hat{I}\pm ,{\hat{I}}^2)$ as components.

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