NMAA07012U Introduction to Operator Algebras (IntroOpAlg)
Volume 2013/2014
Education
MSc Programme in
Mathematics
Content
Commutative
Banach algebras, C*-algebras, commutative C*-algebras, states and
representations, GNS representations, polar decomposition,
non-unital C*-algebras, approximate units and the multiplier
algebra. Towards the end of the course we shall discuss selected
examples of interesting C*-algebras such as the Toeplitz algebra,
AF-algebras, irrational rotation C*-algebras, the Cuntz algebras,
group C*-algebras
Learning Outcome
The
participants are expected to acquire the knowledge listed above in
the course description.
The participants are expected to be able to understand and apply the Gelfand transform and the GNS-construction, they must understand basic facts about order. They must have some familiarity with important examples of C*-algebras.
The participants are expected to master the most fundamental concepts and constructions for C*-algebras which are are used in further studies in operator algebras and in non-commutative geometry
The participants are expected to be able to understand and apply the Gelfand transform and the GNS-construction, they must understand basic facts about order. They must have some familiarity with important examples of C*-algebras.
The participants are expected to master the most fundamental concepts and constructions for C*-algebras which are are used in further studies in operator algebras and in non-commutative geometry
Academic qualifications
Functional Analysis
(FunktAn) and Analysis 2 (An2) or similar introductory courses on
functional analysis and analysis
Teaching and learning methods
5 hours of lectures plus 3
hours of tutorials per week in 8 weeks (last assignment is due in
week 9).
Workload
- Category
- Hours
- Exam
- 20
- Lectures
- 40
- Preparation
- 122
- Theory exercises
- 24
- Total
- 206
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Continuing Education - click here!
Exam
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThere will be given 3 assignments, each of which will count equally towards the final grade.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
- Re-exam
- Oral examination. Several internal examiners
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAA07012U
- Credit
- 7,5 ECTS
- Level
- Full Degree MasterBachelor
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- C
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Mikael Rørdam (6-767376686571447165786c326f7932686f)
Phone + 45 35 32 06 93, office
04.4.21
Saved on the
30-04-2013