The $L_\infty$-algebra of a symplectic manifold

Bas Janssens, Leonid Ryvkin and Cornelia Vizman

Vol. 314 (2021), No. 1, 81–98

DOI: 10.2140/pjm.2021.314.81

Abstract

We construct an $L_{\infty }$-algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to the universal central extension of the Lie algebra of Hamiltonian vector fields.

Keywords

symplectic, Poisson, Lie-infinity, central extension, homotopy Lie algebra

Mathematical Subject Classification

Primary: 53D05, 53D17

Secondary: 17A42, 17B66

Milestones

Received: 15 June 2021

Accepted: 11 July 2021

Published: 15 October 2021