2003/02/04 by Dmitry Roytenberg
Mathematics · #math.QA #math.SG
published as J. Nonlinear Math. Phys., volume 9, no. 3 (2002) 347-356 · arxiv version is already official
arxiv created 2003/02/04 · arxiv updated 2009/11/30
We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant Poisson structures on the homogeneous space S2=CP1=SU(2)/U(1), where SU(2) is endowed with its standard Poisson--Lie group structure,thus extending the result of Ginzburg \citeGin1 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 S2; another corollary is that these structures do not admit smooth rescaling.