Constructing New Braided $T$-categories over Monoidal Hom-Hopf Algebras

Abstract

Let $Au{t}_{mHH}(H)$ denote a set of all automorphisms of a monoidal Hopf algebra $H$ with bijective antipode in the sense of Caenepeel S. and Goyvaerts I. (Commun. Algebra 39, 2216-2240, 2011) and let $G$ be a crossed product group $Au{t}_{mHH}(H)\times Au{t}_{mHH}(H)$. The main aim of this paper is to provide further examples of braided $T$-category in the sense of Turaev (1994, 2008). For this purpose, we first introduce a class of new categories ${}_H{\mathcal{M}\mathcal{H}\mathcal{YD}}^H(A,B)$ of monoidal Hom $(A,B)$-Yetter-Drinfeld modules with $A,B\in Au{t}_{mHH}(H)$. Then we show that the category $\mathcal{M}\mathcal{H}\mathcal{YD}(H)=\{{}_H{\mathcal{M}\mathcal{H}\mathcal{YD}}^H(A,B){\}}_{(A,B)\in G}$ forms a braided $T$-category, generalizing the main constructions construction by Panaite and Staic (Isr J Math 158:349-365, 2007).

References in corpus (1)

• On $G$--equivariant modular categories

Cited by in corpus (5)

• A Note on Braided $T$-categories over Monoidal Hom-Hopf Algebras
• Constructing New Braided $T$-Categories via Weak Monoidal Hom-Hopf Algebras
• The construction of braided $T$-category via Yetter-Drinfeld-Long bimodules
• The Hom-Long dimodule category and nonlinear equations
• Hom-Yang-Baxter equations and Hom-Yang-Baxter systems