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Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.
12
votes
Quantum mathematics?
Working in "quantum mathematics" myself, I should tend to defend this teminology a bit ;) The term is clearly motivated by the usage in physics and, nowadays, is typically used in situations where you …
15
votes
Relationship between "different" quantum deformations
This is not at all an innocent question as there are really many notions of "quantizing stuff" around. A systematic comparison is probably not available (yet) for several reasons. Let me just try to i …
4
votes
Deformation quantization of a closed Riemann surface with genus >1
One should definitely take a look at the work of Bordemann, Meinrenken, and Schlichenmaier: they provide a Berezin-Toeplitz inspired deformation quantization for all compact quantizable (i.e. the Kähl …