Correspondence between the category of Poisson manifolds and the category of von Neumann algebras

This paper is devoted to the exploration of a remarkable similarity between Poisson manifolds and von Neumann algebras written by Dimitri Shlyakhtenko, a program largely due to Alan Weinstein. As they observed, many objects in von Neumann algebra theory — the algebras themselves, bimodules, as well as operations involving them, such as tensor products — have analogs in the world of Poisson manifolds. A list of such analogies which collected by Dimitri Shlyakhtenko has been given in this paper.

کلیدواژه ها:

Poisson Manifold ، von Neumann Algebra ، Symplectic Manifold ، Commutator