In and around the origin of quantum groups

Details In and around the origin of quantum groups In and around the origin of quantum groups

2003-09-11

arxiv.org/abs/math/0309199v1

Mathematics

Operator Algebras

36 pages

Scientific paper

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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