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. One-parameter subgroups, the exponential map and its differential. Universal enveloping algebra, Poincaré-Birkhoff-Witt theorem. Hopf algebras and primitive elements.  Baker-Campbell-Hausdorff formula. Construction of Lie groups from Lie algebras, Lie group homomorphisms from Lie algebra homomorphisms. Cartan's theorem on closed subgroups.

Solvable, nilpotent and semi-simple 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