Timeline for Relations between quantum groups at roots of unity, modular representation theory, and physics
Current License: CC BY-SA 4.0
11 events
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| Jun 4, 2020 at 0:35 | history | edited | Yellow Pig | CC BY-SA 4.0 |
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| Jun 3, 2020 at 21:39 | answer | added | Alexander Chervov | timeline score: 2 | |
| Jun 1, 2020 at 18:33 | history | became hot network question | |||
| Jun 1, 2020 at 16:07 | comment | added | Yellow Pig | @SValera Thank you very much! 1) Would you be able to give some links (to preprints, papers, books, questions on MO) about these applications (to anyons, topological phases of matter, fractional quantum Hall effect, topological quantum computers) of quantum groups at roots of unity that you mention? 2) Would you be able to tell if/how the existing research/questions on modular representation theory of Lie algebras have a bearing on these physical applications via the equivalence of certain categories of representations of Lie algebras in pos. char. and quantum groups at roots of unity? | |
| Jun 1, 2020 at 14:58 | comment | added | Sachin Valera | Witten conjectured that every unitary modular tensor category would come from a Chern-Simons-Witten TQFT. Quantum groups at roots of unity provide an algebraic setting for studying anyons and topological phases of matter. Such phenomena are (expected to be) relevant to various physical systems; most notably the fractional quantum Hall effect. A further application of these ideas is in the construction of a 'topological quantum computer' or memory. There's a lot of literature on this topic and several related questions on MO. | |
| Jun 1, 2020 at 11:51 | history | edited | Yellow Pig |
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| Jun 1, 2020 at 11:06 | vote | accept | Yellow Pig | ||
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| Jun 1, 2020 at 11:06 | answer | added | Carlo Beenakker | timeline score: 4 | |
| Jun 1, 2020 at 10:56 | history | edited | Yellow Pig | CC BY-SA 4.0 |
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| Jun 1, 2020 at 10:38 | history | edited | Yellow Pig |
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| Jun 1, 2020 at 10:32 | history | asked | Yellow Pig | CC BY-SA 4.0 |