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)
Mgr. Pavel Novák (seminar tutor)

Guaranteed by

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

Prerequisites (in Czech)

TYP_STUDIA(N)

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

Study Materials
The course can also be completed outside the examination period.

• Enrolment Statistics (recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2019/MU25004