MU:MU08110 Theory of Groups and Algebras

MU08110 Theory of Groups and Algebras

Mathematical Institute in Opava
Summer 2009

Extent and Intensity

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

Guaranteed by

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.