The aim of this course is to present the classification of finite dimensional, complex semisimple Lie algebras.
To obtain this classification the course will cover the following topics: Soluble and Nilpotent Lie Algebra,
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. The
course assumes knowledge of elementary linear algebra and basic group theory.
Recommended texts:
This 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
Pre-requisites
Algebra II would be sufficient background material. Some of the ideas in
Groups and Rings III would be helpful but not necessary.
On-line notes
These days there are lots of notes available on the web. They vary in relevance to this course.
Mathematicians we will meet
These biographies are from the
MacTutor History of Mathematics Archive.
Handouts
Assignments
Last changed Thursday, 21 May, 2009.
© 2009 The University of Adelaide.
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