Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory (Q1305719)
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scientific article; zbMATH DE number 1342951
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory |
scientific article; zbMATH DE number 1342951 |
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Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory (English)
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25 April 2000
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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.
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Hamiltonian systems
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Poisson structures of hydrodynamic type
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Poisson brackets
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topological field theory
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Frobenius algebras
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