Hamiltonian operators in graded formal calculus of variations
type: Item
instance of: scholarly article
title: Hamiltonian operators in graded formal calculus of variations
zbMATH Open document ID: 0609.58010
DOI: 10.1007/BF01077272
publication date: 1986-01-01T00:00:00Z
review text: In this paper, continuing his previous investigations, the author considers the graded variant of the Gel'fand-Dikij formal variational calculus and generalizes some results of Gel'fand and Dorfman regarding the description of the Lie algebra of the Poisson brackets. The obtained description turns out to be connected with the polynomial Poisson algebras, considered by Sklyanin. On the other hand, from it one can derive the superanalogue theorem of Dubrovin-Novikov on the hydrodynamic Hamiltonians.
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 3986214
zbMATH Keywords: Hamiltonian operator
zbMATH Keywords: Lie superalgebra structure
zbMATH Keywords: graded variant of the Gel'fand-Dikij formal variational calculus
zbMATH Keywords: Lie algebra of the Poisson brackets
zbMATH Keywords: hydrodynamic Hamiltonians
author: Yuri L. Daletskii
reviewed by: Yanglian Pan
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3986214