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, fir...

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Bibliographic Details
Published in:arXiv.org 2014-11
Main Authors: You, Miman, Wang, Shuanhong
Format: Article
Language:English
Subjects:
Automorphisms
Braiding
Online Access:Get full text
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Summary: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}.
ISSN:2331-8422