Deformation Quantization of Polynomial Poisson Algebras
| dc.creator | Penkava, Michael | |
| dc.creator | Vanhaecke, Pol | |
| dc.date | 1998-04-03 | |
| dc.date.accessioned | 2026-07-07T05:24:19Z | |
| dc.date.available | 2026-07-07T05:24:19Z | |
| dc.description | This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential operators. We then compute an explicit third order deformation quantization of A and show that it comes from a quantized enveloping algebra. We show that the deformation extends to a fourth order deformation if and only if the quantized enveloping algebra gives a fourth order deformation; moreover we give an example where the deformation does not extend. A correction term to the third order quantization given by the enveloping algebra is computed, which precisely cancels the obstruction. | |
| dc.description | 33 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/9804022 | |
| dc.identifier | http://arxiv.org/abs/math/9804022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76790 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16E40, 16S80, 17B35 | |
| dc.title | Deformation Quantization of Polynomial Poisson Algebras | |
| dc.type | text |