On Lie-Poisson systems
type: Item
instance of: scholarly article
title: On Lie-Poisson systems
zbMATH Open document ID: 0818.58021
DOI: 10.1016/0034-4877(93)90054-I
author: M. Seredyńska
published in: Reports on Mathematical Physics
publication date: 1995-08-08T00:00:00Z
review text: Let \(Q\) be a Lie group and \(K \subset Q\) a subgroup acting on \(T^* Q\) as a symmetry group for a Hamiltonian function \(H\) on \(T^* Q\). The representation \(T^* Q \to Q \times {\mathfrak q}^*\) (where \({\mathfrak q}^*\) is the dual of the Lie algebra \(\mathfrak q\) of \(Q\)) gives a separation of variables for the Hamiltonian system associated to \(H\). After reduction to \(K \times {\mathfrak k}^*\), the Hamiltonian equation in the cotangential variables becomes a so-called Lie-Poisson system. The author discusses some consequences of the invariance and symmetry assumptions and gives a condition for the momentum to be the constant of motion corresponding to the \(K\) symmetry of the Hamiltonian \(H\).
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 704245
zbMATH Keywords: geometric quantization
zbMATH Keywords: invariance
zbMATH Keywords: symmetry
zbMATH Keywords: momentum
zbMATH Keywords: Lie-Poisson system
MaRDI profile type: Publication
cites work: Q5580321
cites work: Primitive ideals in enveloping algebras
cites work: Q3696183
cites work: Q4109839
cites work: The local structure of Poisson manifolds
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description: scientific article; zbMATH DE number 704245