منابع مشابه
Double Construction for Crossed Hopf Coalgebras
Recently, Turaev [19, 20] (see also Le and Turaev [8] and Virelizier [23]) generalized the notion of a TQFT and Reshetikhin-Turaev invariants to the case of 3-manifolds endowed with a homotopy classes of maps to K(π, 1), where π is a group. One of the key points in [19] is the notion of a crossed Hopf π-coalgebra, here called a Turaev coalgebra or, briefly, a T-coalgebra (see Section 1). As one...
متن کاملFull Crossed Products by Hopf C∗-algebras
We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.
متن کاملTannaka Reconstruction for Crossed Hopf Group Algebras
We provide an analog of Tannaka Theory for Hopf algebras in the context of crossed Hopf group coalgebras introduced by Turaev. Following Street and our previous work on the quantum double of crossed structures, we give a construction, via Tannaka Theory, of the quantum double of crossed Hopf group algebras (not necessarily of finite type).
متن کاملInvolutory Hopf Group-coalgebras and Flat Bundles over 3-manifolds
Given a group π, we use involutary Hopf π-coalgebras to define a scalar invariant of flat π-bundles over 3-manifolds. When π = 1, this invariant equals to the one of 3-manifolds constructed by Kuperberg from involutary Hopf algebras. We give examples which show that this invariant is not trivial.
متن کاملA Categorical Approach to Turaev’s Hopf Group-coalgebras
We show that Turaev’s group-coalgebras and Hopf group-coalgebras are coalgebras and Hopf algebras in a symmetric monoidal category, which we call the Turaev category. A similar result holds for group-algebras and Hopf group-algebras. As an application, we give an alternative approach to Virelizier’s version of the Fundamental Theorem for Hopf algebras. We introduce Yetter-Drinfeld modules over ...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 2013
ISSN: 0386-5991
DOI: 10.2996/kmj/1372337522