discipline 
MSC in
Mathematics, Pure Mathematics, Elective Course

subject 
Lie Groups and Lie Algebras

lecturers 
Dr. Balázs Csikós (associate professor) Dr. Gyula Lakos (teaching assistant) Dr. Gábor Moussong (assistant professor) Dr. László Verhóczki (associate professor) 
credits 
2 
period 
1st semester 
curriculum 
Lie groups,
local Lie groups and their Lie algebras. Oneparameter subgroups, the
exponential map and its differential. Universal enveloping algebra,
PoincaréBirkhoffWitt theorem. Hopf algebras and primitive elements. BakerCampbellHausdorff formula. Construction
of Lie groups from Lie algebras, Lie group homomorphisms from Lie algebra
homomorphisms. Cartan's theorem on closed subgroups. Solvable, nilpotent and semisimple Lie algebras.
Radical, nilradical. Jacobson's theorem, Engel's theorem. Irreducible linear
Lie algebras, reductive Lie algebras. Lie's theorem on linear solvable Lie
algebras. Killing form. Cartan's
criteria for solvability and semisimplicity. Cohomologies of Lie algebras. Theorems
of Whitehead and their applications. Ado's theorem. 
literature 
M. M. Postnikov, Lie Groups
and Lie Algebras. Lectures in
Geometry. Semester V, Mir, Moscow, 1986. J. P. Serre, Lie algebras and
Lie groups, 2nd ed., Springer, 1992. 
form of tuition 
Two hours
of lecture per week. 
mode of assessment 
oral exam 