# Tannaka Reconstruction for Crossed Hopf Group Coalgebras

@article{Zunino2006TannakaRF, title={Tannaka Reconstruction for Crossed Hopf Group Coalgebras}, author={Marcos Zunino}, journal={arXiv: Quantum Algebra}, year={2006} }

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).

## References

SHOWING 1-10 OF 33 REFERENCES

Ribbon graphs and their invaraints derived from quantum groups

- Mathematics
- 1990

The generalization of Jones polynomial of links to the case of graphs inR3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum…

Quantum Groups

- Mathematics
- 1994

Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups…

Quantum Groups

- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…

Quantum Invariants of Knots and 3-Manifolds

- Physics
- 1994

This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of…

Double construction for monoidal categories

- Mathematics
- 1995

One of the most important mathematical achievements of the last decade has been the theory of quantum groups created by V. Drinfeld, M. Jimbo, and others. Quantum groups provide an algebraic…

Homotopy field theory in dimension 3 and crossed group-categories

- Mathematics
- 2000

A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group $\pi$, we introduce…

AN INTRODUCTION TO TANNAKA DUALITY AND QUANTUM GROUPS

- Mathematics
- 1991

The goal of this paper is to give an account of classical Tannaka duality [C⁄] in such a way as to be accessible to the general mathematical reader, and to provide a key for entry to more recent…

Homotopy field theory in dimension 2 and group-algebras

- Mathematics
- 1999

We apply the idea of a topological quantum field theory (TQFT) to maps from manifolds into topological spaces. This leads to a notion of a (d+1)-dimensional homotopy quantum field theory (HQFT) which…