Vol. 314, No. 1, 2021

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

Bas Janssens, Leonid Ryvkin and Cornelia Vizman

Vol. 314 (2021), No. 1, 81–98
Abstract

We construct an L-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.

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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
Authors
Bas Janssens
Delft University of Technology
Delft
The Netherlands
Leonid Ryvkin
Georg-August-Universität Göttingen
Göttingen
Germany
Cornelia Vizman
West University of Timisoara
Timisoara
Romania