Operator algebras and groupoid C*-algebras - NMMA652

• Title: Operátorové algebry a C*-algebry příslušné grupoidům
• Guaranteed by: Department of Mathematical Analysis (32-KMA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2023
• Semester: summer
• E-Credits: 3
• Hours per week, examination: summer s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: Tristan Bice; Karen Strung

Annotation

English

Last update: doc. RNDr. Pavel Pyrih, CSc. (17.07.2021)

An introduction to the main concepts in C*-algebra theory, with the aim at preparing students to understand elements of contemporary research in the field. In particular, later parts of the course will focus on constructions from topological groupoids, a highly active area of research.

Czech

Last update: doc. RNDr. Pavel Pyrih, CSc. (17.07.2021)

Úvod teorie C*-algeber s cílem připravit studenty porozumět základům současného výzkumu v oboru. V druhé polovině semestru se zaměříme na konstrukce C*-algeber příslušných topologickým grupoidům.

Course completion requirements

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (20.07.2021)

The course is finished by an exam.

Literature

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (20.07.2021)

G. J. Murphy, C*-Algebras and Operator Theory

K. R. Strung, An introduction to C*-algebras and the classification program

K. R. Davidson, C*-algebras by Example

J. Renault, A groupoid approach to C*-algebras

Requirements to the exam

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (20.07.2021)

The students could choose between a seminar on a topic of self study or a standard oral examination from the topics presented during the semester.

Syllabus

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (20.07.2021)

1. Basic definitions and Examples

2. Gelfand-Naimark and continuous functional calculus

3. Positive elements, positivity and partial order

4. Hereditary C*-subalgebras

5. Functionals and representations

6. GNS construction

7. Representations

8. Completely positive maps

9. Tensor products

10. Inductive limits and AF algebras

11. Group C*-algebras

12. Crossed products

13. Groupoids

14. Groupoid C*-algebras

15. Twisted groupoid C*-algebras and Cartan subalgebras

Some suggested self-study topics:

1. Cantor minimal systems

2. graph C*-algebras

3. classification AF algebras

4. Compact quantum groups

5. Cuntz algebras

Entry requirements

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (20.07.2021)

Basic functional analysis