Poisson morphisms and reduced affine Poisson group actions
type: Item
instance of: scholarly article
title: Poisson morphisms and reduced affine Poisson group actions
zbMATH Open document ID: 1032.53074
author: Qilin Yang
publication date: 2003-05-05T00:00:00Z
review text: The symmetry reduction appearing in the study of classical dynamical systems is studied from an abstract point of view. The concept of quotient Poisson group is introduced and some basic properties are established. Then, the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson G-variety V is studied. It is emphasized that if the quotient Poisson varieties are considered as reduced phase spaces, then the quotient affine Poisson group action may be considered as the symmetry reduction in stages. The Poisson morphisms, including equivalent cases, between Poisson affine varieties are also discussed. It is suggested that the results presented in this paper can be applied to the study of algebraic integrable systems.
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 1885830
zbMATH Keywords: Poisson affine varieties
zbMATH Keywords: affine Poisson groups
zbMATH Keywords: Poisson morphisms
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
full work available at URL: s101140200158
OpenAlex ID: W2043003611
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DOI: 10.1007/S101140200158
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1885830