A 2-categorical extension of Etingof-Kazhdan quantisation
| Autor: | Valerio Toledano Laredo, Andrea Appel |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Lie bialgebra
Quantum group General Mathematics 010102 general mathematics Zero (complex analysis) General Physics and Astronomy Associator Field (mathematics) Extension (predicate logic) 01 natural sciences Combinatorics Tensor (intrinsic definition) Mathematics::Category Theory Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics Representation Theory (math.RT) Mathematics::Representation Theory Equivalence (measure theory) Mathematics - Representation Theory Mathematics |
| Zdroj: | Toledano Laredo, V & Appel, A 2018, ' A 2-categorical extension of Etingof–Kazhdan quantisation ', Selecta Mathematica (New Series), vol. 24, no. 4, pp. 3529-3617 . https://doi.org/10.1007/s00029-017-0381-z |
| DOI: | 10.48550/arxiv.1610.09744 |
| Popis: | Let k be a field of characteristic zero. Etingof and Kazhdan constructed a quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice of an associator Phi. They prove moreover that this quantisation is functorial in b. Remarkably, the quantum group U_h(b) is endowed with a Tannakian equivalence F_b from the braided tensor category of Drinfeld-Yetter modules over b, with deformed associativity constraints given by Phi, to that of Drinfeld-Yetter modules over U_h(b). In this paper, we prove that the equivalence F_b is functorial in b. Comment: Small revisions in Sections 2 and 6. An appendix added on the equivalence between admissible Drinfeld-Yetter modules over a QUE and modules over its quantum double. To appear in Selecta Math. 71 pages |
| Databáze: | OpenAIRE |
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