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Rigidity of Poisson Lie group actions
Miranda Galcerán, Eva
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
n this paper we prove that close infinitesimal momentum maps associated to Poisson Lie actions are equivalent under some mild assumptions. We also obtain rigidity theorems for actual momentum maps (when the acting Lie group G is endowed with an arbitrary Poisson structure) combining a rigidity result for canonical Hamiltonian actions (\cite{MMZ}) and a linearization theorem(\cite{GW}). These results have applications to quantization of symmetries since these infinitesimal momentum maps appear as the classical limit of quantum momentum maps (\cite{BEN}).
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Geometry, Algebraic
Geometria algebraica
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Article - Draft
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