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Geometric structures related to W*=algebras, Lecture I
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 m 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.