Invariant Poisson Realizations and the Averaging of Dirac Structures

Symmetry Integrability and Geometry-Methods and Applications

article

José A. Vallejo¹  Yurii Vorobiev² 

[1] Universidad Autónoma de San Luis Potosí;Universidad de Sonora

关键词: Poisson structures;    Dirac structures;    geometric data;    averaging operators;   

DOI  :  10.3842/SIGMA.2014.096

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown