Dirac pairs

Yvette Kosmann-Schwarzbach

doi:10.3934/jgm.2012.4.165

Article Contents

2012, Volume 4, Issue 2: 165-180. Doi: 10.3934/jgm.2012.4.165

This issue Previous Article Variational Integrators for Hamiltonizable Nonholonomic Systems Next Article A property of conformally Hamiltonian vector fields; Application to the Kepler problem

Dirac pairs

Yvette Kosmann-Schwarzbach^1,

1.
Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau

Received: March 31, 2011

Published: May 2012

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Abstract

We extend the definition of the Nijenhuis torsion of an endomorphism of a Lie algebroid to that of a relation, and we prove that the torsion of the relation defined by a bi-Hamiltonian structure vanishes. Following Gelfand and Dorfman, we then define Dirac pairs, and we analyze the relationship of this general notion with the various kinds of compatible structures on manifolds, more generally, on Lie algebroids.

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Mathematics Subject Classification: Primary: 17B63, 53D17; Secondary: 18B10, 70G45.

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