# Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets

Carlet, Guido, Casati, Matteo, Shadrin, Sergey (2017) Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets. Journal of Geometry and Physics, 114 . pp. 404-419. ISSN 0393-0440. (doi:10.1016/j.geomphys.2016.12.008)

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https://dx.doi.org/10.1016/j.geomphys.2016.12.008

## 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 nonvanishing in D > 1. Hence, in contrast with the D = 1 case, the deformation theory in the multivariable case is non-trivial.

Item Type: Article 10.1016/j.geomphys.2016.12.008 Poisson cohomology; poisson brackets of hydrodynamic type; deformations of poisson structure Q Science > QA Mathematics (inc Computing science) > QA440 Geometry Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Matteo Casati 28 Feb 2019 12:00 UTC 14 Jan 2020 09:33 UTC https://kar.kent.ac.uk/id/eprint/67927 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-2207-4807