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15 February 2002 A Darboux theorem for Hamiltonian operators in the formal calculus of variations
Ezra Getzler
Duke Math. J. 111(3): 535-560 (15 February 2002). DOI: 10.1215/S0012-7094-02-11136-3

Abstract

We prove a formal Darboux-type theorem for Hamiltonian operators of hydrodynamic type, which arise as dispersionless limits of the Hamiltonian operators in the KdV and similar hierarchies. We prove that the Schouten Lie algebra is a formal differential graded Lie algebra, which allows us to obtain an analogue of the Darboux normal form in this context.

We include an exposition of the formal deformation theory of differential graded Lie algebras $\mathfrak {g}$ concentrated in degrees $[-1,\infty)$; the formal deformations of $\mathfrak {g}$ are parametrized by a 2-groupoid that we call the Deligne 2-groupoid of $\mathfrak {g}$, and quasi-isomorphic differential graded Lie algebras have equivalent Deligne 2-groupoids.

Citation

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Ezra Getzler. "A Darboux theorem for Hamiltonian operators in the formal calculus of variations." Duke Math. J. 111 (3) 535 - 560, 15 February 2002. https://doi.org/10.1215/S0012-7094-02-11136-3

Information

Published: 15 February 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1100.32008
MathSciNet: MR1885831
Digital Object Identifier: 10.1215/S0012-7094-02-11136-3

Subjects:
Primary: 32G34
Secondary: 37K05, 55P62

Rights: Copyright © 2002 Duke University Press

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Vol.111 • No. 3 • 15 February 2002
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