From subfactors to categories and topology. II. The quantum double of tensor categories and subfactors

@article{Mueger2001FromST,
  title={From subfactors to categories and topology. II. The quantum double of tensor categories and subfactors},
  author={Michael Mueger},
  journal={Annals of Probability},
  year={2001}
}
  • Michael Mueger
  • Published 19 November 2001
  • Mathematics
  • Annals of Probability

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References

SHOWING 1-10 OF 64 REFERENCES

Quantum Invariants of Knots and 3-Manifolds

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

The Structure of Sectors¶Associated with Longo–Rehren Inclusions¶I. General Theory

Abstract: We investigate the structure of the Longo–Rehren inclusion for a finite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic

Spherical Categories

A bstract. T his paper is a study ofm onoidalcategories w ith duals w here the tensor product need not be com m utative. T he m otivating exam ples are categories of representations ofH opfalgebras.

Drinfel’d: On almost cocommutative Hopf algebras

  • Leningrad Math. J. 1,
  • 1990

Quantum Groups

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

A duality for Hopf algebras and for subfactors. I

We provide a duality between subfactors with finite index, or finite dimensional semisimple Hopf algebras, and a class ofC*-categories of endomorphisms.

Braided Groups and Quantum Fourier Transform

Abstract We show that acting on every finite-dimensional factorizable ribbon Hopf algebra H there are invertible operators S , T obeying the modular identities ( S T )3 = λ S 2, where λ is a

Tangles and Hopf algebras in braided categories

Reshetikhin & V

  • G. Turaev: Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103, 547-598
  • 1991
...