The relation between local and global dual pairs

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

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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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
Depositing User:	Dr James Montaldi
Date Deposited:	25 Oct 2005
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/9

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