Entry requirements

120 credits including 90 credits in mathematics. Linear Algebra II. Participation in Algebraic Structures and Differential Topology. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• give an account of the following concepts: differentiable manifold, vector field and Lie bracket,
• explain the concepts of topological group and Lie group and give examples of such groups,
• use the Baker-Campbell-Hausdorff formula,
• describe the Lie algebra of a given Lie group,
• translate properties of the Lie algebra to properties of the associated Lie group.

Content

Lie groups, especially closed subgroups of the real and the complex general linear group.. Classical families of simply connected compact groups. Lie algebras. The Lie algebra of vector fields associated to a Lie group. The exponential map. Baker-Campbell-Hausdorff's formula. The relation between a Lie group and its corresponding Lie algebra. The universal cover of a Lie group. Homogeneous spaces.

Instruction

Lectures and problem solving sessions.

Assessment

Home assignments and oral examination.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course cannot be incluced in the same degree as the courses Lie groups 1MA048 or Lie groups 1MA567.