Abstract
In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.
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Chiara Esposito was supported by a CAST exchange grant in one of her visits to Barcelona. CAST (Contact and Symplectic Topology) was a network supported by the European Science Foundation.
Eva Miranda is supported by the Ministerio de Economía y Competitividad project with reference: MTM2015-69135-P (MINECO/FEDER) and by the AGAUR (Generalitat de Catalunya) project SGR 2014SGR634.
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Esposito, C., Miranda, E. Rigidity of infinitesimal momentum maps. Isr. J. Math. 219, 757–781 (2017). https://doi.org/10.1007/s11856-017-1497-8
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DOI: https://doi.org/10.1007/s11856-017-1497-8