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Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras

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      Abstract

      We introduce and study some mixed product Poisson structures on product manifolds associated to Poisson Lie groups and Lie bialgebras. For quasitriangular Lie bialgebras, our construction is equivalent to that of fusion products of quasi-Poisson G-manifolds introduced by Alekseev, Kosmann- Schwarzbach, and Meinrenken. Our primary examples include four series of holomorphic Poisson structures on products of flag varieties and related spaces of complex semi-simple Lie groups.

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      Journal
      2015-04-26
      2016-01-11
      1504.06843

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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      37 pages, submitted to IMRN
      math.DG

      Geometry & Topology

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