# MA453 Lie Algebras

**Lecturer: **Adam Thomas

**Term(s):** Term 2

**Status for Mathematics students:** List C. Suitable for Year 3 MMath

**Commitment:** 30 Lectures

**Assessment:** 3 hour exam (85%), Assessed Work (15%)

**Prerequisites: **Algebra I and Algebra II, although having taken some 3rd year Algebra modules in addition would be advantageous.

**Leads To: **

**Content**: Lie algebras are related to Lie groups, and both concepts have important applications to geometry and physics. The Lie algebras considered in this course will be finite dimensional vector spaces over endowed with a multiplication which is almost never associative (that is, the products and are different in general). A typical example is the -dimensional vector space of all complex matrices, with *Lie product* defined as the commutator matrix . The main aim of the course is to classify the building blocks of such algebras, namely the simple Lie algebras of finite dimension over .

**Books**:

J.E. Humphreys, *Introduction to Lie algebras and representation theory*, Springer, 1979

T.O. Hawkes, *Lie algebras*, Notes available from Maths Dept.

N. Jacobson, *Lie algebras*, Dover, 1979