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Geometric structures related to W*=algebras, Lecture Ⅲ
时间  Datetime
 
地点  Venue
报告人  Speaker
Anatol Odzijewicz
单位  Affiliation
University of Bialystok, Poland
邀请人  Host
Tudor Stefan Ratiu
报告摘要  Abstract

In this series of fourlectures I will define and investigate in the framework of Banach differentialgeometry the geometric structures related in a canonical way to the structureof a W*-algebra m

(vonNeumann algebra).These are the following structures:

(1)   The Banach Liegroupoid G(m)of partial invertible elements of whosemanifold of units  is the lattice oforthogonal projections L(m).

(2)   TheBanach Lie algebroid A(m)àL(m)of the groupoid G(m).

(3)   Thevarious fiberwise linear Poisson structures and the Poisson VB-groupoidsnaturally related to m.

The obtainedresults show that the methods of Poisson geometry can be applied to thedescription of the classical as well as quantum physical systems.