Group Theory 2 1100-2`TG2
The theory of Lie groups and algebras plays one of the central roles in contemporary mathematics and finds a lot of applications in theoretical physics (in the field theory, relativity, the theory of elementary particles etc.). This course will be devoted mainly to the theory of Lie algebras which are "infinitesimal objects" corresponding to Lie groups and which contain "the most" of the information about the latter ones.
Program:
1. Elementy krystalografii
2. Lie algebras.
3. Description of irreducible representations of the su(n) algebras (based on the example of su(2) and su(3)).
4. Applications to high energy physics
--classification of particles according to SU(3)
--grand unified theories
--spinor formalism for the Lorentz group
Student's work load:
Lectures: 30 h -- 1ECTS
Preparation for lectures: 30 h -- 1 ECTS
Preparation for the exam: 30 h -- 1 ECTS
Course coordinators
Learning outcomes
Knowledge: Familiarity with the foundations of the theory of Lie algebras and groups.
Skills: Solving problems using elements of the theory of Lie algebras and groups, especially concerning their representations.
Attitude: Appreciation of the beauty, depth and usefulness
of the theory of Lie algebras and groups, especially in the context of applications to physics.
Assessment criteria
Oral exam
Practical placement
does not apply
Bibliography
1. J. F. Adams, Lectures on Lie groups, Benjamin, 1969.
2. S. Helgason, Differential geometry, Lie groups, and symmetric spaces, AMS, 1978.
3. A. A. Kirillov, Elements of the theory of representations, Springer-Verlag, 1976.
4. W. Wojtyński, Grupy i algebry Liego, PWN, 1986.
5. A. Trautman "Grupy oraz ich reprezentacje" (skrypt WF UW)
6. J.Dereziński "Teoria grup" http://www.fuw.edu.pl/~derezins/teoriagrup.pdf
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: