Poisson algebra of 2d dimensionally reduced gravity

D. Bernard; N. Regnault

Poisson algebra of 2d dimensionally reduced gravity

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arxiv hep-th/0002207 v2 pith:QGLTHLJR submitted 2000-02-24 hep-th nlin.SI

D. Bernard , N. Regnault This is my paper · ORCID

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keywords equationspoissonreducedaffinealgebraalgebrasboundariesbrackets

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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.

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Integrable deformations of dimensionally reduced gravity
hep-th 2025-02 conditional novelty 6.0 of 10

Auxiliary field and Yang-Baxter deformations of D=2 dimensionally reduced gravity are shown to admit flat Lax representations, with the auxiliary field case preserving the Hamiltonian integrability structure.

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