Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory
type: Item
instance of: scholarly article
title: Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory
zbMATH Open document ID: 0934.37056
DOI: 10.1016/S0034-4877(99)80032-9
published in: Reports on Mathematical Physics
publication date: 2000-04-25T00:00:00Z
review text: The problem of classification of compatible Poisson structures of hydrodynamic type, i.e. compatible local first-order homogeneous Poisson brackets in field theory is studied. The author shows that all two-component compatible Poisson structures of hydrodynamic type are classified by means of the solutions of a homogeneous four-component system of hydrodynamic type. He proves that the two-component reduction of this system is related to the equations of associativity in two-dimensional topological field theory. It is also true in the case of deformations of two special Frobenius algebras.
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 37K30
zbMATH DE Number: 1342951
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Poisson structures of hydrodynamic type
zbMATH Keywords: Poisson brackets
zbMATH Keywords: topological field theory
zbMATH Keywords: Frobenius algebras
author: O. I. Mokhov
MaRDI profile type: Publication
cites work: Q4862319
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full work available at URL: s0034-4877(99)80032-9
OpenAlex ID: W2073397864
description: scientific article; zbMATH DE number 1342951