A darboux theorem for hamiltonian operators in the formal calculus of variations

Ezra Getzler*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

82 Scopus citations

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 g concentrated in degrees [−1, ∞); the formal deformations of g are parametrized by a 2-groupoid that we call the Deligne 2-groupoid of g, and quasiisomorphic differential graded Lie algebras have equivalent Deligne 2-groupoids.

Original languageEnglish (US)
Pages (from-to)535-560
Number of pages26
JournalDuke Mathematical Journal
Volume111
Issue number3
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)

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