Symplectic algebroids, groupoid Toeplitz operators and deformation quantization
arXiv:2604.10370
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.
23 pages, comments are welcome !