MATS1990 Lie groups (4 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

Description

Differentiable manifolds, Lie bracket, Lie groups, Lie algebras, Lie homomorphisms, exponential map; (possibly: adjoint representation, Haar measure, homogenous manifolds).

Learning outcomes

After passing the course successfully the student

  • can recognize different isomorphic versions of Lie groups
  • knows the abstract version of concepts such as the tangent space and derivative
  • can apply central results of the theory such as the exponential and logarithm functions
  • can connect to each other properties of Lie groups and Lie algebras
  • knows how these results are used e.g. in the construction of representations and the classification of Lie groups

Description of prerequisites

Introduction to manifolds

Literature

  • John M. Lee:Introduction to smooth manifolds. Graduate Texts in Mathematics 218, Springer, 2006. ISBN 978-0-387-95448-6

Completion methods

Method 1

Evaluation criteria:
Course exam and exercises
Select all marked parts

Method 2

Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x

Participation in teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
No published teaching
x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
No published teaching