# Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets

Abstract : We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin–Novikov type with $D$ independent variables. We find that the second and third cohomology groups are generically non-vanishing in $D > 1$ . Hence, in contrast with the $D = 1$ case, the deformation theory in the multivariable case is non-trivial.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01660609
Contributor : Imb - Université de Bourgogne <>
Submitted on : Monday, December 11, 2017 - 10:42:42 AM
Last modification on : Wednesday, February 28, 2018 - 11:57:24 AM

### Citation

Guido Carlet, Matteo Casati, Sergey Shadrin. Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets. Journal of Geometry and Physics, Elsevier, 2017, 114, pp.404 - 419. ⟨10.1016/j.geomphys.2016.12.008⟩. ⟨hal-01660609⟩

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