Invariant Poisson Realizations and the Averaging of Dirac Structures

José A. Vallejo ; Yurii Vorobiev

Symmetry, integrability and geometry: methods and applications, Tome 10 (2014)

Résumé

We describe an averaging procedure on a Dirac manifold, with respect to a class of compatible actions of a compact Lie group. Some averaging theorems on the existence of invariant realizations of Poisson structures around (singular) symplectic leaves are derived. We show that the construction of coupling Dirac structures (invariant with respect to locally Hamiltonian group actions) on a Poisson foliation is related with a special class of exact gauge transformations.

Détail

Keywords: Poisson structures; Dirac structures; geometric data; averaging operators.

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