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2005.6: The relation between local and global dual pairs

2005.6: J Montaldi, J-P Ortega and TS Ratiu (2004) The relation between local and global dual pairs. Math Research Letters, 11. pp. 355-363. ISSN 1073-2780

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Official URL: http://www.mrlonline.org/mrl/2004-011-003/2004-011-003-007.pdf

Abstract

In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis (this is well known), while the converse requires a dimension condition (which appears not to be known). We also provide examples illustrating the necessity of the extra conditions.

Item Type:Article
Additional Information:

Copyright International Press

Uncontrolled Keywords:Poisson geometry, dual pairs.
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 53 Differential geometry
MIMS number:2005.6
Deposited By:Dr James Montaldi
Deposited On:25 October 2005

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