| Abstract: |
| A symplectic groupoid of real unipotent upper-triangular matrices was introduced by A.Bondal.
It consists of pairs of nondegenerate matrix $B$ and unipotent upper-triangular matrix $A$ such that $BAB^t$ is also unipotent upper-triangular. The symplectic groupoid possesses a natural symplectic structure that induces a natural Poisson structure on the space of unipotent upper-triangular matrices. This Poisson structure appeared earlier in papers by B.Dubrovin, M.Ugaglia, M.Mazzocco and other in relation to isomonodromic deformations.
We discuss a cluster structure compatible with this Poisson structure and use it to describe a
cluster structure on Teichmuller space of closed genus 2 curve. |
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