Symplectic algebroids, groupoid Toeplitz operators and deformation quantization
Symplectic Geometry
2026-04-14 v1 Differential Geometry
Operator Algebras
Abstract
We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are defined on groupoids whose algebroid can be endowed with a Heisenberg group structure on the fibers. This generalizes an approach due to Guillemin and Melrose in the symplectic case.
Cite
@article{arxiv.2604.10370,
title = {Symplectic algebroids, groupoid Toeplitz operators and deformation quantization},
author = {Clément Cren and Jean-Marie Lescure and Omar Mohsen},
journal= {arXiv preprint arXiv:2604.10370},
year = {2026}
}
Comments
23 pages, comments are welcome !