| Abstrakt: |
The ranknswapping multifraction algebra is a field of cross ratios up to (n + 1) × (n + 1) -determinant relations equipped with a Poisson bracket, called the swapping bracket, defined on the set of ordered pairs of points of a circle using linking numbers. Let D k be a disk with k points on its boundary. The moduli space X PGL n , D k is the building block of the Fock–Goncharov X moduli space for any general surface. Given any ideal triangulation of D k , we find an injective Poisson algebra homomorphism from the rank n Fock–Goncharov algebra for X PGL n , D k to the rank n swapping multifraction algebra with respect to the Atiyah–Bott–Goldman Poisson bracket and the swapping bracket. Two such injective Poisson algebra homomorphisms related to two ideal triangulations T and T ′ are compatible with each other under the flips. [ABSTRACT FROM AUTHOR] |
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