Requirements/prerequisites: MA2215, MA2322 desirable, concurrent registration for MA3411
Duration: 11 weeks (Michaelmas Term)
Number of lectures per week: 3 including tutorials
ECTS credits: 5
End-of-year Examination: 2 hour exam in Trinity Term (April/May)
Lie algebras should be thought of as the infinitesimal analogue of groups. Lie theory is an important and very active branch of mathematics with many links to other areas: geometry, representation theory, mathematical physics amongst others.
Definitions, small examples, classical Lie algebras, subalgebras, ideals and homomorphisms.
Refer to http://www.maths.tcd.ie/~rtange/teaching/lie_algebras/Lie_algebras.html for further details.
Learning Outcomes: On sucessful completion of this module, students will be able to:
Give the definitions of: Lie algebra, homomorphism of Lie algebras, subalgebra, ideal, derivation, centre, representation of a Lie algebra, submodule, irreducible module, homomorphism of g-modules, the Killing form of a Lie algebra and the trace form of a classical Lie algebra, the derived and descending central series of a Lie algebra, nilpotent Lie algebra, solvable Lie algebra, solvable radical, semisimple and simple Lie algebra, maximal toral subalgebra, root system, irreducible root system.