Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
classification
🧮 math.DG
math-phmath.MPnlin.SI
keywords
cohomologypoissoncasedubrovin-novikovscalarbracketbracketscompute
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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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