Subject: Lie Groups and Lie Algebras	Code: MG012	

Semester	 Hours: C+S+L	Type	 Section	
7	2+2+0	optional	Mathematics	
7	2+2+0	optional	Mathematics-Computer Science	

Teaching Staff in Charge	Assoc.Prof. PINTEA Cornel, Ph.D., cpintea@math.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.
	
Selective 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%)