Poisson Cohomology of SU(2)-Covariant "Necklace" Poisson Structures on S2

DOI

10.2991/jnmp.2002.9.3.7How to use a DOI?

Abstract

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 Poisson­Lie group structure, thus extending the result of Ginzburg [2] on the Bruhat­Poisson 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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Dmitry Roytenberg
PY  - 2002
DA  - 2002/08/01
TI  - Poisson Cohomology of SU(2)-Covariant "Necklace" Poisson Structures on S2
JO  - Journal of Nonlinear Mathematical Physics
SP  - 347
EP  - 356
VL  - 9
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.3.7
DO  - 10.2991/jnmp.2002.9.3.7
ID  - Roytenberg2002
ER  -