On classification of discrete, scalar-valued Poisson Brackets

Emanuele Parodi

doi:10.1016/j.geomphys.2012.05.004

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arXiv · 1109.4327

On classification of discrete, scalar-valued Poisson Brackets

Emanuele Parodi

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Abstract

We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be reduced to cubic PB of standard Volterra lattice by discrete Miura-type transformations. Finally, improving a consolidation lattice procedure, we obtain new families of non-degenerate, vector-valued and first order dDGPBs, which can be considered in the framework of admissible Lie-Poisson group theory.

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Emanuele Parodi. 2011-09-20. On classification of discrete, scalar-valued Poisson Brackets. https://doi.org/10.1016/j.geomphys.2012.05.004

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