Lie groups and algebras |
ter |
|||||
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, applications, exercices and problems the theoretical materiale given at the course. |
Content |
1. Topological groups. Basic properties.
2. Classical groups. 3. Integration on compact groups. 4. Groups of transformations. 5. Lie groups. 6. Lie algebras of finite dimension 7. Nilpotent and rezoluble Lie algebras. |
References |
1. Doubrovine, B., Novikov, S., Fomenko, A., Geometrie contemporaine. Methodes et applications, Mir, Moscou, 1982
2. Kawakubo, K., The theory of transformation groups, Oxford, New York, Tokyo, Oxford University Press, 1991 3. L. Nicolescu, Lectii de Grupuri Lie, Univ. Bucuresti, 1984. 4. Postnikov, M.M., Groupes et algebres de Lie, Editions Mir, Moscou, 1985. 5. Tarina, M. Grupuri Lie, Cluj-Napoca, 1987. 6. Verona, A., Introducere in coomologia algebrelor Lie, Ed. Acad R.S.R. |
Assessment |
Exam. |