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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  \C endowed with a multiplication which is almost never associative (that is, the products  (ab)c and a(bc) are different in general). A typical example is the  n^2 -dimensional vector space of all  n\times n complex matrices, with Lie product  [A,B] defined as the commutator matrix  [A,B]=AB-BA . The main aim of the course is to classify the building blocks of such algebras, namely the simple Lie algebras of finite dimension over  \C .


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

Additional Resources

Archived Pages: Pre-2011 2012 2015 2016 2018

Year 1 regs and modules
G100 G103 GL11 G1NC

Year 2 regs and modules
G100 G103 GL11 G1NC

Year 3 regs and modules
G100 G103

Year 4 regs and modules

Archived Material
Past Exams
Core module averages