Dirac pairs | Zendy

Yvette Kosmann–Schwarzbach | Zendy

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Dirac pairs

Author(s) -

Yvette Kosmann–Schwarzbach

Publication year - 2012

Publication title -

the journal of geometric mechanics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.511

H-Index - 17

eISSN - 1941-4897

pISSN - 1941-4889

DOI - 10.3934/jgm.2012.4.165

Subject(s) - lie algebroid , poisson manifold , mathematics , tangent bundle , pure mathematics , torsion (gastropod) , poisson bracket , algebra over a field , manifold (fluid mechanics) , dirac (video compression format) , hamiltonian (control theory) , lie algebra , symplectic geometry , physics , quantum mechanics , medicine , neutrino , mechanical engineering , mathematical optimization , surgery , engineering , tangent space

International audienceWe 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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