arXiv subjects

Miman You

Publications and source records attributed to Miman You.

3 recordsLinked to original sources

arXiv2017

A New approach to the construction of braided T-categories

The aim of this paper is to construct a new braided $T$-category via the generalized Yetter-Drinfel'd modules and Drinfel'd codouble over Hopf algebra, an approach different from that proposed by Panaite and Staic \cite{PS}. Moreover, in the case of finite dimensional, we will show that this category coincides with the corepresentation of a certain coquasitriangular Turaev group algebra that we construct. Finally we apply our theory to the case of group algebra.

math.QA↗

arXiv2014

A Note on Braided $T$-categories over Monoidal Hom-Hopf Algebras

Let $ Aut_{mHH}(H)$ denote the set of all automorphisms of a monoidal Hopf algebra $H$ with bijective antipode in the sense of Caenepeel and Goyvaerts \cite{CG2011}. The main aim of this paper is to provide new examples of braided $T$-category in the sense of Turaev \cite{T2008}. For this, first we construct a monoidal Hom-Hopf $T$-coalgebra $\mathcal{MHD}(H)$ and prove that the $T$-category $Rep(\mathcal{MHD}(H))$ of representation of $\mathcal{MHD}(H)$ is isomorphic to $\mathcal {MHYD}(H)$ as braided $T$-categories, if $H$ is finite-dimensional. Then we construct a new braided $T$-category $\mathcal{ZMHYD}(H)$ over $\mathbb{Z},$ generalizing the main construction by Staic \cite{S2007}.

math.RA↗

arXiv2014

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

Let $ Aut_{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 $ Aut_{mHH}(H)\times Aut_{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 $_{H}\mathcal {MHYD}^{H}(A, B)$ of monoidal Hom $(A, B)$-Yetter-Drinfeld modules with $A, B \in Aut_{mHH}(H)$. Then we show that the category ${\cal MHYD}(H)=\{{}_{H}\mathcal {MHYD}^{H}(A, B)\}_{(A, B)\in G}$ forms a braided $T$-category, generalizing the main constructions construction by Panaite and Staic (Isr J Math 158:349-365, 2007).

math.RA↗