NMAK13014U Operator Algebras: Lifting Problems

Volume 2013/2014
Education
MSc Programme in Mathematics
Content
The course is structured around the notion of lifting problems in operator algebras.  A multitude of methods are introduced to show the participants how to solve selected lifting problems and to provide insight into central methods in operator algebras.

The course employs and strengthens the participants' knowledge from IntroOpAlg, and when the course ends, the participants will have encountered most of the classical constructions in operator algebras.

The course covers the following topics.
  • Multiplier and corona algebras,
  • Universal C*-algebras,
  • Projectivity and semiprojectivity,
  • Brown-Douglas-Fillmore theory - introduction to topological methods in operator theory,
  • Extension groups,
  • Nuclear C*-algebras and lifting of completely-positive maps
Learning Outcome
Knowledge
Properties of multiplier and corona algebras, universality in C*-algebras, BFD-theory, nuclearity and completely positive maps, and the notions of projectivity and semiprojectivity for C*-algebras.

Skills
Use functional calculus/spectral theory as well as completeness.

Competence
Employ objects such as multiplier and corona algebras, completely-positive maps and nuclear algebras to prove lifting results for elements of C*-algebras.  Classify essentially normal operators (BDF-theory) and the functor Ext.  Be able to apply corona algebra technique and extension theory for solving concrete lifting problems.
Literature
Notes will be handed out.
Introduction to operator algebras (IntroOpAlg).
4 hours lectures and 2 hours excercises each week.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 92
  • Project work
  • 60
  • Theory exercises
  • 18
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Pass/fail based on 4 compulsory handins during the course.
Marking scale
passed/not passed
Censorship form
No external censorship
Re-exam
Reexam: 30 minutes oral exam, internal censorship, pass/ fail.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.