Poisson algebra of 2d dimensionally reduced gravity
arXiv:hep-th/0002207 · doi:10.1088/1126-6708/2000/05/017
Abstract
Using a Lax pair based on twisted affine $sl(2,R)$ 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.
16 pages, minor corrections. To appear in JHEP