The paper reviews the construction of a fiber functor for the Finkelberg-Kazhdan-Lusztig equivalence and discusses its consequences for the structure of weak Hopf algebras and unitarizability of braided fusion categories from conformal field theory.
In and around the origin of quantum groups
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abstract
Quantum groups were invented largely to provide solutions of the Yang-Baxter equation and hence solvable models in 2-dimensional statistical mechanics and one-dimensional quantum mechanics. They have been hugely successful. But not all Yang-Baxter solutions fit into the framework of quantum groups. We shall explain how other mathematical structures, especially subfactors, provide a language and examples for solvable models. The prevalence of the Connes tensor product of Hilbert spaces over von Neumann algebras leads us to speculate concerning its potential role in describing entangled or interacting quantum systems.
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The braided Doplicher-Roberts program and the Finkelberg-Kazhdan-Lusztig equivalence: A historical perspective, recent progress, and future directions
The paper reviews the construction of a fiber functor for the Finkelberg-Kazhdan-Lusztig equivalence and discusses its consequences for the structure of weak Hopf algebras and unitarizability of braided fusion categories from conformal field theory.
- Constructing equivalences between quantum group fusion categories and Huang-Lepowsky modular categories via quantum gauge groups