MU25004 Algebraic Structures in Geometry

Mathematical Institute in Opava
Winter 2019
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
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.
The course is also listed under the following terms Summer 2013, Summer 2014, Summer 2015, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (recent)
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