Publication Date:
2014-11-05
Description:
Let A u t m H H ( H ) denote the set of all automorphisms of a monoidal Hopf algebra H with bijective antipode in the sense of Caenepeel and Goyvaerts [“Monoidal Hom-Hopf algebras,” Commun. Algebra39, 2216–2240 (2011)] and let G be a crossed product group A u t m H H ( H ) × A u t m H H ( H ) . The main aim of this paper is to provide new examples of braided T -category in the sense of Turaev [“Crossed group-categories,” Arabian J. Sci. Eng., Sect. C33(2C), 483–503 (2008)]. For this purpose, we first introduce a class of new categories MHYD H H ( A , B ) of ( A , B )-Yetter-Drinfeld Hom-modules with A , B ∈ A u t m H H ( H ) . Then we construct a category M H Y D ( H ) = { MHYD H H ( A , B ) } ( A , B ) ∈ G and show that such category forms a new braided T -category, generalizing the main constructions by Panaite and Staic [“Generalized (anti) Yetter-Drinfel'd modules as components of a braided T-category,” Isr. J. Math.158, 349–366 (2007)]. Finally, we compute an explicit new example of such braided T -categories.
Print ISSN:
0022-2488
Electronic ISSN:
1089-7658
Topics:
Mathematics
,
Physics
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