The L∞-algebra of a symplectic manifold

@article{Janssens2021TheLO,
  title={The L∞-algebra of a symplectic
manifold},
  author={Bas Janssens and L. M. Ryvkin and Cornelia Vizman},
  journal={Pacific Journal of Mathematics},
  year={2021}
}
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. 

References

SHOWING 1-10 OF 37 REFERENCES
Universal Central Extension of the Lie Algebra of Hamiltonian Vector Fields
We determine the universal central extension of the Lie algebra of hamiltonian vector fields, thereby classifying its central extensions. Furthermore, we classify the central extensions of the Lie
Models for classifying spaces and derived deformation theory
Using the theory of extensions of L∞ algebras, we construct rational homotopy models for classifying spaces of fibrations, giving answers in terms of classical homological functors, namely the
Integrability of central extensions of the Poisson Lie algebra via prequantization
We present a geometric construction of central S^1-extensions of the quantomorphism group of a prequantizable, compact, symplectic manifold, and explicitly describe the corresponding lattice of
A differential complex for Poisson manifolds
Construction du complexe canonique d'une variete de Poisson. Homologie canonique des varietes symplectiques. Application a l'homologie de Hochschild des algebres non commutatives
The sh Lie Structure of Poisson Brackets in Field Theory
Abstract:A general construction of an sh Lie algebra (L∞-algebra) from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson
Strongly homotopy Lie algebras
The present paper can be thought of as a continuation of the paper "Introduction to sh Lie algebras for physicists" by T. Lada and J. Stasheff (International Journal of Theoretical Physics Vol. 32,
L∞-Algebras from Multisymplectic Geometry
A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n + 1. In previous work with Baez and Hoffnung, we described
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