Reference : Rank n swapping algebra for PGLn Fock--Goncharov X moduli space
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Rank n swapping algebra for PGLn Fock--Goncharov X moduli space
Sun, Zhe mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] Poisson algebra homomorphism ; rank n swapping algebra ; Fock–Goncharov X moduli space
[en] The rank n swapping algebra is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of (K^n×K^{n∗})^r/GL(n,K). For any ideal triangulation of D_k---a disk with k points on its boundary, using determinants, we find an injective Poisson algebra homomorphism from the fraction algebra generated by the Fock--Goncharov coordinates for X_{PGL_n,D_k} to the rank n swapping multifraction algebra for r=k⋅(n−1) with respect to the (Atiyah--Bott--)Goldman Poisson bracket and the swapping bracket. This is the building block of the general surface case. Two such injective Poisson algebra homomorphisms related to two ideal triangulations T and T′ are compatible with each other under the flips.
FnR ; FNR13242285 > Zhe Sun > > COmbinatorial and ALgebraic Aspects of Surface group representations. > 01/09/2018 > 31/08/2020 > 2017

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