MAT9460 – C*-algebras
Course description
Schedule, syllabus and examination date
Course content
The course gives an introduction to C*-algebras and von Neumann algebras, which are the most important classes of operator algebras. Such algebras have fundamental applications in various areas of mathematics and in quantum physics. After having covered the basic results in the theory, some important classes of examples will be studied. The choice of examples may vary from one year to another, depending on the interests of the students following the course.
Learning outcome
After completing the course you
- are familiar with the definitions of C*-algebras and von Neumann algebras, and with basic related concepts, such as *-homomorphisms, ideals, quotients, approximate units and multiplier algebras
- know about the positive cone of a C*-algebra, how it induces an order on the self-adjoint elements and how it is used to define states
- know how to construct the GNS-representation associated with a state and how to represent a C*-algebra faithfully as bounded operators on a Hilbert space
- know the connection between pure states and irreducible representations of a C*-algebra;
- have a good understanding of several operator topologies and know how to characterize von Neumann algebras with the help of double commutants
- can describe C*-algebras of compact operators and have a knowledge of other important classes of C*-algebras.
Admission to the course
PhD candidates from the Faculty of Mathematics and Natural Sciences at the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
Overlapping courses
- 10 credits overlap with MAT4460 – C*-algebras.
- 10 credits overlap with MAT9360 – C*-algebras (continued).
- 10 credits overlap with MAT4360 – C*-algebras (continued).
Teaching
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
Final written exam or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 1 October/1 March for the autumn semester and the spring semester respectively.
This course has 1 mandatory assignment that must be approved before you can sit the final exam.
In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4460 – C*-algebras
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.