MU25004 Algebraic Structures in Geometry

Mathematical Institute in Opava
Summer 2013
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Tomáš Kopf, Ph.D.
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
Syllabus (in Czech)
  • 1. Kvaterniony.
    2. Algebry a jejích reprezentace.
    3. Maticové grupy.
    4. Lieovy grupy, Lieovy algebry a jejich reprezentace.
    5. Příklady: O(3), grupy izometrií, SU(2), SL(2,R).
    6. Poznámky ke klasifikaci Lieových grup.
    7. Homogenní prostory a symetrie.
    8. Speciální funkce: sférické harmoniky.
    9. Cliffordovy algebry a jejich reprezentace.
    10. Spinory.
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
English
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2014, Summer 2015, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Summer 2013, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2013/MU25004