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Poisson algebra of 2d dimensionally reduced gravity

Abstract

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

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