"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Lie Groups and Lie Algebras
Code
Semes-
ter
Hours: C+S+L
Type
Section
MG012
7
2+2+0
optional
Matematica
MG012
7
2+2+0
optional
Matematică-Informatică
Teaching Staff in Charge
Assoc.Prof. PINTEA Cornel, Ph.D.,  cpinteamath.ubbcluj.ro
Aims
The course introduce and develope the main rations and results in the theory of Lie groups and Lie algebras. This theory is an important instrument in solving some problems in differential geometry and theoretical physics. The seminars cover by examples,
Content
I. TOPOLOGICALLY GROUPS
1. Elementary properties of topologically groups
2. Topologically groups of transformations
II. LIE GROUPS
1. The definition of Lie groups. Exponential application.
2. One parameter subgroups. Lie subgroups. The classical Lie groups.
3. Diferential structures on orbit spaces.
4. The characterization theorem of connected abelian Lie groups.
5. Maximal Torus.
III. Lie Algebras
1. Generalities
2. Nilpotent and solvable Lie Algebras.
3. Biliniar mappings and semisimple Lie algebras.

References
1. DOUBROVINE, B., NOVIKOV, S., FOMENKO, A., Geometrie contemporaine. Methodes et applications, Mir, Moscou, 1982.
2. GHEORGHIEV, GH., OPROIU, V., Varietati finit si infinit dimensional, Vol. I si II, Ed. Acad. R.S.R, 1976 respectiv 1979.
3. KAWAKUBO, K., The theory of transformation groups, Oxford, New York, Tokyo, Oxford University Press, 1991
4. VERONA, A., Introducere in coomologia algebrelor Lie, Ed. Acad. R.S.R., Bucuresti 1974.
Assessment
Reports(50%)+Exam(50%).
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject