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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

In and around the origin of quantum groups

Vaughan F. R. Jones This is my paper
classification math.OA math-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

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