Quasitriangular Hopf group algebras and braided monoidal categories
نویسندگان
چکیده
منابع مشابه
Weak Hopf Monoids in Braided Monoidal Categories
We develop the theory of weak bimonoids in braided monoidal categories and show them to be quantum categories in a certain sense. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid R leads to a weak Hopf monoid R ⊗ R.
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This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided categories. Such objects generalise super-algebras and super-Hopf algebras, as well as colour-Lie algebras. Basic facts about braided categories C are recalled, the modules and comodules of Hopf algebras in such categories are studied, the notion of ‘braided-commutative’ or ‘braided-cocommutative’ Hop...
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We study (Hopf) bialgebras in a braided category, which are equipped with an inner twist. By means of the inner twist we define the second mutiplication on the (Hopf) bialgebra, which plays the role of the opposite multiplication. Hence one can define the coquasitriangular structure on these bialgebras. Examples of these bialgebras are reconstructed bialgebras.
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We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. That is, the category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2014
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-014-0142-5