# Invariant Poisson Realizations and the Averaging of Dirac Structures

```@article{Vallejo2014InvariantPR,
title={Invariant Poisson Realizations and the Averaging of Dirac Structures},
author={Jos{\'e} Antonio Vallejo and Yu. Vorobiev},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2014},
volume={10},
pages={096}
}```
• Published 3 May 2014
• Mathematics
• Symmetry Integrability and Geometry-methods and Applications
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.
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Preface 1. Introduction Part I. Differential Geometry of Singular Spaces: 2. Differential structures 3. Derivations 4. Stratified spaces 5. Differential forms Part II. Reduction of Symmetries: 6.