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Cotangent bundle reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand…
Poisson reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in Poisson reduction. The article recalls most the necessary prerequisites to understand the main…
Symmetry and symplectic reduction
Juan-Pablo Ortega, Tudor S. Ratiu
This encyclopedia article briefly reviews without proofs some of the main results in symplectic reduction. The article recalls most the necessary prerequisites to understand the ma…
Symplectic leaves in real Banach Lie-Poisson spaces
Daniel Beltiţă, Tudor S. Ratiu
We present several large classes of real Banach Lie-Poisson spaces whose characteristic distributions are integrable, the integral manifolds being symplectic leaves just as in fini…
Extensions of Banach Lie-Poisson spaces
Anatol Odzijewicz, Tudor Ratiu
The extension of Banach Lie-Poisson spaces is studied and linked to the extension of a special class of Banach Lie algebras. The case of W*-algebras is given particular attention.…
The relation between local and global dual pairs
James Montaldi, Juan-Pablo Ortega, Tudor S. Ratiu
In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage fro…