The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.
Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.RT 1years
2025 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Double Poisson (vertex) algebra cohomology
The authors define a completed double Poisson cohomology valid for all double Poisson brackets, and introduce three cohomology theories for double Poisson vertex algebras, with representation functor compatibility.