2000/02/21 by Ezra Getzler, Getzler, Ezra · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #14B20 #37K10 #53D17 #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Logic, programming, and type systems #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG #msc:14B20 #msc:37K10 #msc:53D17 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0002164
openalex publication_date 2000/02/21 · arxiv created 2000/08/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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,∞) 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).