Poisson cohomology of SU(2)-covariant 'necklace' Poisson structures on S^{2}
| dc.creator | Roytenberg, Dmitry | |
| dc.date | 2003-02-04 | |
| dc.date.accessioned | 2026-07-07T04:54:54Z | |
| dc.date.available | 2026-07-07T04:54:54Z | |
| dc.description | We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant Poisson structures on the homogeneous space S^{2}=CP^{1}=SU(2)/U(1), where SU(2) is endowed with its standard Poisson--Lie group structure,thus extending the result of Ginzburg \cite{Gin1} on the Bruhat--Poisson structure which is a member of this family. In particular, we compute several invariants of these structures, such as the modular class and the Liouville class. As a corollary of our computation, we deduce that these structures are nontrivial deformations of each other in the direction of the standard rotation-invariant symplectic structure on S^{2}; another corollary is that these structures do not admit smooth rescaling. | |
| dc.description | arxiv version is already official | |
| dc.identifier | https://arxiv.org/abs/math/0302036 | |
| dc.identifier | http://arxiv.org/abs/math/0302036 | |
| dc.identifier | J. Nonlinear Math. Phys., volume 9, no. 3 (2002) 347-356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66438 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Symplectic Geometry | |
| dc.title | Poisson cohomology of SU(2)-covariant 'necklace' Poisson structures on S^{2} | |
| dc.type | text |