Journal of Nonlinear Mathematical Physics

Volume 9, Issue 3, August 2002, Pages 347 - 356

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

Authors
Dmitry Roytenberg
Corresponding Author
Dmitry Roytenberg
Received 19 December 2001, Accepted 15 April 2002, Available Online 1 August 2002.
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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 3
Pages
347 - 356
Publication Date
2002/08/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2002.9.3.7How to use a DOI?
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/).

Cite this article

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  -