Invariant poisson realizations and the averaging of dirac structures

José A. Vallejo; Yurii Vorobiev

doi:10.3842/SIGMA.2014.096

Invariant poisson realizations and the averaging of dirac structures

José A. Vallejo^*, Yurii Vorobiev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Article number	096
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	10
DOIs	https://doi.org/10.3842/SIGMA.2014.096
State	Published - 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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10.3842/SIGMA.2014.096

Cite this

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AB - 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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KW - Geometric data

KW - Poisson structures

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DO - 10.3842/SIGMA.2014.096

M3 - Artículo

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ER -

Invariant poisson realizations and the averaging of dirac structures

Abstract

Bibliographical note

Keywords

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