65 citations · 78 across the 3 of their papers we have counts for
11 papers · 1 filter
Functorial quantization and the Guillemin-Sternberg conjecture
N. P. Landsman
We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The `quantization…
Quantization and the tangent groupoid
N. P. Landsman
This is a survey of the relationship between C*-algebraic deformation quantization and the tangent groupoid in noncommutative geometry, emphasizing the role of index theory. We fir…
Quantization as a functor
N. P. Landsman
Notwithstanding known obstructions to this idea, we formulate an attempt to turn quantization into a functorial procedure. We define a category PO of Poisson manifolds, whose objec…
Bicategories of operator algebras and Poisson manifolds
N. P. Landsman
It is well known that rings are the objects of a bicategory, whose arrows are bimodules, composed through the bimodule tensor product. We give an analogous bicategorical descriptio…
Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids
N. P. Landsman
It is well known that a measured groupoid G defines a von Neumann algebra W*(G), and that a Lie groupoid G canonically defines both a C*-algebra C*(G) and a Poisson manifold A*(G).…
Quantized reduction as a tensor product
N. P. Landsman
Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplec…