Abstract
Using a Lax pair based on the affine SL(2,) Kac-Moody algebra, we solve two-dimensional reduced vacuum Einstein's equations. We obtain explicit determinant formulae for metric coefficients with no quadrature left. This Lax connection also allows a new approach to the Poisson algebra of two-dimensional reduced gravity. In particular, we show that it leads to pure c-number r-matrices and modified Yang-Baxter equations. We explain how one can construct classical observables within this framework.
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