6533b838fe1ef96bd12a5076

RESEARCH PRODUCT

Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

Guido CarletHessel PosthumaSergey Shadrin

subject

Mathematics - Differential GeometryFOS: Physical sciencesPoisson distribution01 natural sciencessymbols.namesakePoisson bracketMathematics::Quantum Algebra0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics::Representation TheoryMathematics::Symplectic GeometryMathematical PhysicsPencil (mathematics)MathematicsAlgebra and Number TheoryNonlinear Sciences - Exactly Solvable and Integrable Systems010102 general mathematicsMathematical analysisInfinitesimal deformationMathematical Physics (math-ph)Cohomology[ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]Nonlinear Sciences::Exactly Solvable and Integrable SystemsDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]symbols010307 mathematical physicsGeometry and TopologyExactly Solvable and Integrable Systems (nlin.SI)Analysis

description

We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.

yearjournalcountryeditionlanguage
2015-01-18
https://dx.doi.org/10.48550/arxiv.1501.04295