MU08110 Theory of Groups and Algebras

Mathematical Institute in Opava
Summer 2011
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
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
The structure of groups and algebras is presented with special attention to representations and further generalizations.
Syllabus
  • Groups, G-modules, representation of groups, tensor product, reducibility, irreducibility, complete reducibility. Representations of finite groups, characters, group algebra. Representations of symmetric groups, Young tableaux, representations of alternating groups. Lie groups and Lie algebras, representations of Lie groups and Lie algebras, representations of the algebra sl(2, C). Classical Lie algebras, semisimple Lie algebras, Killing form, Weyl group, Cartan subalgebra, roots, Cartan's classification of (semi)simple Lie algebras. Representations of algebras sl(n, C), Weyl's construction. Representations of symplectic algebras sp(2n, C). Clifford algebras, representations of orthogonal algebras so(n, C), spinors. Real, Spinor and quaternionic representations. Quantum groups and their representations, Lie superalgebras and their representations.
Literature
    recommended literature
  • K. Erdmann, M. Wildon. Introduction to Lie algebras. Springer, 2006. info
  • C. Isham. Modern Differential Geometry for Physicists. Singapore, 1999. info
  • 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.
Teacher's information
Oral exam; further requirements to be specified in the course of the semester.
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 2010, Summer 2012.
  • Enrolment Statistics (Summer 2011, recent)
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