# 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