Lie Algebras IV 2009

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Description

This course will present the classification of finite dimensional, complex, semisimple Lie algebras. These objects are of fundamental importance in mathematics and physics. Topics covered will include: Soluble and Nilpotent Lie Algebras, structure theory of Lie algebras, Cartan subalgebras of semisimple Lie algebras, root systems and their classification by means of Dynkin diagrams and the classification of simple, complex Lie algebras.

Pre-requisites

A knowledge of elementary linear algebra and group theory as contained in Algebra II will be sufficient. Groups and Rings III would be useful but not necessary.

Recommended texts:

The course will be based on the textbook

Introduction to Lie Algebras
(Springer Undergraduate Mathematics Series)
Karin Erdmann, Mark J. Wildon

This in the Barr-Smith Library with call number: 512.5543 E667i. There is also a copy on reserve.

Other books covering this material would also be good such as the more advanced but standard

Introduction to Lie Algebras and Representation Theory
(Springer Graduate Texts in Mathematics)
James E. Humphries

On-line notes

These days there are lots of notes available on the web. They vary in relevance to this course.

Notes by Sternberg.
Notes by Samelson.

Mathematicians we will meet

These biographies are from the MacTutor History of Mathematics Archive.