8 papers
Symplectic algebroids, groupoid Toeplitz operators and deformation quantization
Clément Cren, Jean-Marie Lescure, Omar Mohsen
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 def…
Families of Toeplitz operators, family index and deformation quantization
Clément Cren, Erfan Rezaei
Given a contact fibration, we construct smooth families of formal Szegö projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these op…
Stratification of the Helffer-Nourrigat Cone
Clément Cren
Given a singular filtration on a manifold, e.g., a sub-Riemannian setting, one can understand the regularity problems through the Androulidakis-Mohsen-Yuncken pseudodifferential ca…
Fields of Toeplitz algebras form the principal symbol of regular 2-step nilpotent groups
Clément Cren
We show that the C*-algebra of a regular 2-step nilpotent lie group can be recovered using continuous fields of Toeplitz algebras and a crossed product. We generalize this result t…
Toeplitz algebras and the Heisenberg group
Clément Cren
We show an isomorphism between an algebra which is naturally constructed from the Toeplitz algebra generated by d-shifts, and an ideal of the C * -algebra of the (2d + 1)-dimension…
Transverse parabolic structures and transverse BGG sequences
Clément Cren
Manifolds endowed with a parabolic geometry in the sense of Cartan come with natural sequences of differential operators and their analysis provide the so called (curved) BGG seque…
Filtered Calculus and crossed products by R-actions
Clément Cren
We show an isomorphism between the kernel of the C*-algebra of the tangent groupoid of a filtered manifold and the crossed product of the order 0 pseudodifferential operators in th…
A transverse index theorem in the calculus of filtered manifolds
Clément Cren
We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of tran…