MATH42112/62112 - Lie Algebras (21/22)

Level

Undergraduate Course

University

University of Manchester

Prerequisites

Algebraic Structures 2 (MATH20212)

Duration

12 weeks (2 lectures per week lasting 50 minutes each)

Lectures

Mon at 1:00pm in Alan Turing G.114/Fri at 9:00am Roscoe 4.4

Office Hours

Unless announced otherwise my office hour will be held 2pm - 3pm every Thursday in Alan Turing Building 1.111. If you need to see me outwith this office hour then please make an appointment by email.

Textbook Sources

For background on linear algebra the following textbooks are recommended:

• Sheldon Axler, Linear algebra done right (third edition), Undergraduate Texts in Mathematics, Springer, Cham, 2015.
• Thomas S. Blyth and Edmund F. Robertson, Further linear algebra, Springer Undergraduate Mathematics Series, Springer-Verlag London, Ltd., London, 2002.
• Thomas S. Blyth and Edmund F. Robertson, Basic linear algebra, Springer Undergraduate Mathematics Series, Springer-Verlag London, Ltd., London, 1998.

For further reading on Lie Algebras then you can look at the following texts:

• Karin Erdmann and Mark J. Wildon, Introduction to Lie Algebras, Springer Undergraduate Mathematics Series, Springer-Verlag London Limited, 2006.
• J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, Springer, 1972.

Syllabus

• The Jordan Decomposition of a linear endomorphism
• Flags and Representations of Lie Algebras
• Nilpotent Lie Algebras and Engel's Theorem
• Solvable Lie Algebras and Lie's Theorem
• The Killing Form and Cartan's Criteria
• Representations of sl2
• The abstract Jordan decomposition