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Using a Lax pair based on twisted affine $sl(2,R)$ Kac-Moody and Virasoroalgebras, we deduce a r-matrix formulation of two dimensional reduced vacuumEinstein's equations. Whereas the fundamental Poisson brackets arenon-ultralocal, they lead to pure c-number modified Yang-Baxter equations. Wealso describe how to obtain classical observables by imposing reasonableboundaries conditions.Comment: 16 pages, minor corrections. To appear in JHE

Poisson algebra of 2d dimensionally reduced gravity