Invariant poisson realizations and the averaging of dirac structures

José A. Vallejo*, Yurii Vorobiev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Article number096
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume10
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014 Institute of Mathematics. All rights reserved.

Keywords

  • Averaging operators
  • Dirac structures
  • Geometric data
  • Poisson structures

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