Invariant quantization in one and two parameters on semisimple coadjoint orbits of simple Lie groups
| dc.creator | Donin, Joseph | |
| dc.creator | Gurevich, Dmitry | |
| dc.creator | Shnider, Steve | |
| dc.date | 1998-07-28 | |
| dc.date | 1998-08-12 | |
| dc.date.accessioned | 2026-07-07T05:25:33Z | |
| dc.date.available | 2026-07-07T05:25:33Z | |
| dc.description | We study one and two parameter quantizations of the function algebra on a semisimple orbit in the coadjoint representation of a simple Lie group subject to the condition that the multiplication on the quantized algebra is invariant under action of the Drinfeld-Jimbo quantum group. We prove that the corresponding Poisson bracket must be the sum of the so-called R-matrix bracket and an invariant bracket. We classify such brackets for all semisimple orbits and show that they form a family of dimension equal to the rank equal to the second cohomology group of the orbit and then we quantize these brackets. A two parameter (or double) quantization corresponds to a pair of compatible Poisson brackets: the first is as described above and the second is the Kirillov-Kostant-Souriau bracket on the orbit. Not all semisimple orbits admit a compatible pair of Poisson brackets. We classify the semisimple orbits for which such pairs exist and construct the corresponding two parameter quantization of these pairs in some of the cases. | |
| dc.description | 23 pages, Latex, no figures; Assumption p.12, remarks 3.2 and 4.1 revised | |
| dc.identifier | https://arxiv.org/abs/math/9807159 | |
| dc.identifier | http://arxiv.org/abs/math/9807159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77219 | |
| dc.subject | Quantum Algebra | |
| dc.title | Invariant quantization in one and two parameters on semisimple coadjoint orbits of simple Lie groups | |
| dc.type | text |