Course - Introduction to Lie Theory - MA3407
MA3407 - Introduction to Lie Theory
Lessons are not given in the academic year 2021/2022
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.
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. The course will be given in autumn in years of even numbers.
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.
Information about course material will be given at the start of the course.
Credits: 7.5 SP
Study level: Second degree level
Language of instruction: English, Norwegian
- Topology and Geometry
Department with academic responsibility
Department of Mathematical Sciences
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"