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MA453 Content

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 .

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