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- W2008366475 abstract "We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grassmannian is viewed as a Poisson homogeneous space of the general linear group equipped with an appropriate R-matrix Poisson–Lie structure. We also prove that the Poisson brackets on the Grassmannian arising in this way are compatible with the natural cluster algebra structure." @default.
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- W2008366475 date "2009-04-25" @default.
- W2008366475 modified "2023-10-07" @default.
- W2008366475 title "Poisson geometry of directed networks in a disk" @default.
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- W2008366475 doi "https://doi.org/10.1007/s00029-009-0523-z" @default.
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