01138nas a2200121   4500008004100000245007900041210006900120260001000189520073700199653002500936100001900961856003600980       2013                        en  d00aOn deformations of multidimensional Poisson brackets of hydrodynamic  type0 adeformations of multidimensional Poisson brackets of hydrodynami  bSISSA3 aThe theory of Poisson Vertex Algebras (PVAs) is a good framework to treat
Hamiltonian partial differential equations. A PVA consist of a pair
$(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra
$\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend
the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$
commuting derivations. We call this structure a multidimensional PVA: it is a
suitable setting to the study of deformations of the Poisson bracket of
hydrodynamic type associated to the Euler's equation of motion of
$d$-dimensional incompressible fluids. We prove that for $d=2$ all the first
order deformations of such class of Poisson brackets are trivial.10aHamiltonian operator1 aCasati, Matteo  uhttp://hdl.handle.net/1963/7235