A Darboux theorem for Hamiltonian operators in the formal calculus of variations

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dc.creatorGetzler, Ezra
dc.date2000-02-21
dc.date2000-08-10
dc.date.accessioned2026-07-07T04:33:58Z
dc.date.available2026-07-07T04:33:58Z
dc.descriptionWe prove a Darboux theorem for formal deformations of Hamiltonian operators of hydrodynamic type (Dubrovin-Novikov). Not all deformations are equivalent to the original operator: there is a moduli 2-stack of normal forms. The paper utilizes three main concepts: 1) dg Lie algebras concentrated in degrees [-1,\infty) such as the Schouten algebra - these give a convenient language for describing deformation problems; 2) the Deligne 2-groupoid associated to such a dg Lie algebra, which represents the moduli of formal deformations; 3) a refined version of the Schouten bracket in the formal calculus of variations, due to V. O. Soloviev (hep-th/9305133).
dc.identifierhttps://arxiv.org/abs/math/0002164
dc.identifierhttp://arxiv.org/abs/math/0002164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58729
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.subject37K10; 53D17; 14B20
dc.titleA Darboux theorem for Hamiltonian operators in the formal calculus of variations
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