Examination arrangement

Course content

The course gives a basic introduction to Lie algebras and their connections to various aspects of group theory: discrete groups, algebraic groups, and (of course) Lie groups. The main focus will be on the examples given by matrices, because the general theory can often be reduced to these by means of representation theory. Possible specific topics are: Lie algebras, universal enveloping algebras, free, nilpotent, solvable, and semi-simple Lie algebras; Lie groups, vector fields and integration, one-parameter groups and the exponential map, homogeneous spaces, Clifford algebras and spinor groups.

Learning outcome

1. Knowledge. The student is able to articulate and explain the basic concepts and ideas behind Lie theory, and to elucidate their meaning using examples and application of algebraic or analytic nature.

2. Skills. The student has an overall understanding of Lie groups and Lie algebras. They can formulate problems and carry out simple calculations of Lie-theoretical nature, especially by reduction to matrix groups in lower dimensions.

Learning methods and activities

The learning methods and activities depend on the course teacher.
The lectures will be given in English if the course is attended by students who don't master a Scandinavian language. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments. Oral examination, unless agreed otherwise.

Further on evaluation

In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety. Submitted work that counts towards the final grade will also have to be retaken. For more information about grading and evaluation, see "Teaching methods and activities".

Recommended previous knowledge

It is advantageous to have knowlegde about linear algebra and analysis beyond the basic courses. Furthermore, some basic knowlegde about topology is an advantage.

Course materials

Information about course material will be given at the start of the course.