Welcome to the public home page of

MAT4142/MAT5143: Introduction to Lie Algebras

(Fall 2009)

Instructor: Erhard Neher

  • The course will start on Wednesday, September 9th, 13:00 in KED B005 (building of the Department of Mathematics and Statistics). In the meantime you can have a look at the course outline. I look forward to seeing you there!

  • Textbook for MAT 4142: Karin Erdmann and Mark J. Wildon, Introduction to Lie Algebras, published by Springer-Verlag in the Springer Undergraduate Mathematics Series

  • Textbook for MAT 5143: James Humphreys, Introduction to Lie Algebras and Representation Theory, published by Springer-Verlag Both books are available in the University Bookstore, but of course also through other suppliers.

  • Since the course is cross-listed with a 4th year course, the lectures will be given at the 4th year level. Graduate students will be assigned extra reading material and exercises from the graduate text book.

  • This course is strongly recommended for any undergraduate student interested in doing a summer research project or an M.Sc. thesis under my supervision.

  • Official course description of MAT4142/MAT5143: Structure of solvable, nilpotent and semisimple finite dimensional Lie algebras. Prerequisites: MAT3141 or permission of the instructor.

  • General description of the course for non-experts: The theory of Lie algebras builds on Linear Algebra (hence the prerequisite MAT 3141). Rather than studying a single endomorphism (or matrix) we will look at a whole family of endomorphisms. In order to get a good theory we will assume that the family is in fact a vector space (a subspace of the vector space of endomorphisms) which is closed under the commutator product [A,B] = AB-BA. In the course we will develop a structure theory for these objects, called Lie algebras. This is one of the fundamental achievements of 20th-century mathematics.

    Lie algebras are the algebraic part of ``Lie theory'', with the theory of Lie groups and the theory of Coxeter groups providing the analytic and combinatorial aspects. In order to take this course, it is however not necessary to have taken the course on Lie groups or Coxeter groups. Much of modern pure mathematics builds on and uses the theory of Lie algebras. The course is therefore an ideal preparation for anybody who would like to pursue graduate studies in pure mathematics.

    Lie algebras is the research area of the instructor and also of my colleagues Nevins, Salmasina and Savage. It is related to the research area of many other professors in the department.

  • This is only a preliminary course web site. The actual course web site will be in Virtual Campus.

  • My home page (some indications on what I do besides teaching MAT 4142/MAT5143)