MA3407 - Introduction to Lie Theory
Lessons are not given in the academic year 2016/2017
The course gives a basic introduction to Lie groups and Lie algebras, and the connection between the two by way of the exponential map. These structures play an important role in modern mathematics, where the term "symmetry" is often expressed mathematically using Lie groups and transformations. The theory will also be presented from a historical perspective. The main focus will be the classical linear groups and algebras and their matrix representations. Examples of applications will be collected from algebra, differential equations, geometry, cybernetics or theoretical physics. The course will next be held in the spring of 2018.
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-geometric nature. The groups SO(3), SU(2) and SO(1,2) are of special interest in their application to classical mechanics, quantum mechanics, and relativity theory, respectively.
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
Lectures and possibly exercises and/or some smaller projects. An oral exam counts for 100% of the final mark. The lectures may be given in English. If the course is taught in English, the exam may be given only in English. Students are free to choose Norwegian or English for written assessments.
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.
- * The location (room) for a written examination is published 3 days before examination date.