Subspace lattices in finite von Neumann algebras

Release:2016-06-21 Viewed:39

Lecture

Lecturer: Prof Wu Wenming (Chongqing normal university)

Theme:Subspace lattices in finite von Neumann algebras

Abstract:The main topic of this talk is on the subspace lattices in a finite von Neumann algebra. We will introduce the definitions of reflexive subspace lattices relative to a finite von Neumann algebra and the *-algebra consisting of the closed operators affiliated with the finite von Neumann algebra. It is shown that this kind reflexive subspace lattice generated by three projections in general position is homeomorphic to the sphere plus two points. We also characterize the automorphisms fixing the subspace lattices determined by three free projections with half trace.

Furthermore, we will briefly introduce some recent progress in transitivity of a small subspace lattice and show that an abelian Kadison-Singer algebra (if there exists) in matrix algebra Mn(C)(n>2) cannot be generated by a single element.

Time:June 17 2016(Friday)1000-1100
Place: 6th classroom