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In and around the origin of quantum groups

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arxiv math/0309199 v1 pith:SCE6WXRO submitted 2003-09-11 math.OA math-phmath.MP

Vaughan F. R. Jones This is my paper · ORCID
classification math.OAmath-phmath.MP
keywords quantumgroupsmechanicsmodelssolutionssolvableyang-baxteralgebras
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Constructing equivalences between quantum group fusion categories and Huang-Lepowsky modular categories via quantum gauge groups

    math.OA 2025-02 unverdicted novelty 7.0 of 10

    The paper announces and outlines a ribbon braided tensor equivalence between quantum group fusion categories and Huang-Lepowsky VOA fusion categories for classical types and G2, with full proofs deferred to a companion paper.

  2. Matrix-product operator dualities in integrable lattice models

    cond-mat.stat-mech 2026-02 accept novelty 6.0 of 10

    MPO dualities with exact inverses transform the R-matrix into an extended R-matrix satisfying a modified Yang–Baxter algebra, while non-invertible dualities preserve the baxterization structure.

  3. The braided Doplicher-Roberts program and the Finkelberg-Kazhdan-Lusztig equivalence: A historical perspective, recent progress, and future directions

    math.OA 2026-02 unverdicted novelty 2.0 of 10

    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 categor...

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