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arXiv · 1410.3361

On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric

Andrea Savoldi
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Abstract

We provide a complete list of two- and three-component Poisson structures of hydrodynamic type with degenerate metric, and study their homogeneous deformations. In the non-degenerate case any such deformation is trivial, that is, can be obtained via Miura transformation. We demonstrate that in the degenerate case this class of deformations is non-trivial, and depends on a certain number of arbitrary functions. This shows that the second Poisson-Lichnerowicz cohomology group does not vanish.

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Andrea Savoldi. 2015-03-09. On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric. https://arxiv.org/abs/1410.3361

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