MU08110 Theory of Groups and Algebras

Mathematical Institute in Opava
Summer 2010
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Kristína Smítalová, 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
Course objectives (in Czech)
Struktura grup a algeber je vysvětlena se speciálním zaměřením na jejich reprezentace a další zobecnění.
Syllabus (in Czech)
  • Grupy, G-moduly, reprezentace grupy, tenzorový součin, reducibilita, ireducibilita, úplná reducibilita. Reprezentace konečných grup, charaktery, grupová algebra. Reprezentace symmetrických grup, Youngovy diagramy, reprezentace alternujících grup. Lieovy grupy a algebry, reprezentace Lieových grup a algeber, reprezentace algebry sl(2,C). Klasické Lieovy algebry, polojednoduché Lieovy algebry, Killingova forma, Weylova grupa, Cartanova podalgebra, kořeny, Cartanova klasifikace Lieovych algeber. Reprezentace algeber sl(n,C), Weylova konstrukce. Reprezentace symplektických algeber sp(2n,C). Cliffordovy algebry, reprezentace ortogonálních algeber so(n,C), spinory. Reálné, spinorové a kvaternionové reprezentace. Kvantové grupy a jejích reprezentace, Lieovy superalgebry a jejích reprezentace.
Literature
    recommended literature
  • J. C. Jantzen. Lectures on quantum groups. Amer. Math. Soc., Providence, 1997. info
  • J. Fuchs, C. Schweigert. Symmetries, Lie algebras and representations. Cambridge University Press, Cambridge, 1997. info
  • W. Fulton, J. Harris. Representation theory: a first course. Springer, Berlin, 1996. info
  • J. F. Cornwell. Group theory in Physics, vol I, II, III. Academic Press, London-New York, 1989. info
  • A. O. Barut, R. Raczka. Theory of group representations and applications. World Scientific, Singapore, 1986. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2011, Summer 2012.
  • Enrolment Statistics (Summer 2010, recent)
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