2003/09/11 by Vaughan F. R. Jones, Jones, Vaughan F. R. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Quantum Mechanics and Applications #math-ph #math.MP #math.OA #msc:17B37 #msc:46L37 #msc:57M25 #msc:81P15 #msc:82B20
paper · pdf · doi:10.48550/arxiv.math/0309199
36 pages
arxiv created 2003/09/11 · arxiv updated 2009/12/01
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.