MU:MU25004 Algebraic Structures in Geom. - Course Information

MU25004 Algebraic Structures in Geometry

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Michal Marvan, CSc. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Geometry and Global Analysis (programme MU, N1101)

Syllabus

• 1. Quaternions.
  2. Algebras and their representations.
  3. Matrix groups.
  4. Lie groups, Lie algebras and their representations.
  5. Examples: O(3), groups of isometries, SU(2), SL(2,R).
  6. Remarks on classification of Lie groups.
  7. Homogeneous spaces and symmetries.
  8. Special functions: spherical harmonics.
  9. Clifford algebras and their representations.
  10. Spinors.
  

Literature

recommended literature
• K. Erdmann, M. Wildon. Introduction to Lie algebras. Springer, 2006. info
• B. C. Hall. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. Springer, 2003. info
• H. B. Lawson, Jr, and M. L. Michelson. Spin Geometry, Princeton Mathematical Series 38. Princeton Univ. Press, Princeton, 1989. info
• P. Budinich and A. Trautman. The Spinorial Chessboard, Trieste Notes in Physics. Springer-Verlag, Berlin, Heidelberg, 1988. info
• A. O. Barut, R. Raczka. Theory of group representations and applications. World Scientific, Singapore, 1986. info
• S. Lang. SL2(R). Graduate Texts in Mathematics, 105. Springer-Verlag, New York, 1985. info

Language of instruction

Czech

Further Comments

The course can also be completed outside the examination period.

• Enrolment Statistics (Winter 2016, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2016/MU25004