Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg

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Seminar: Lie groups, Lie algebras and their representations
Semester
WiSe 2020 / 21

Lecturer
Jonathan Glöckle, Matthias Ludewig

Type of course (Veranstaltungsart)
Seminar

Contents
Lie groups are important to describe symmetries, both in mathematics and in application (physics,
chemistry, engineering, ...). The classical Lie groups are for example the orthogonal groups O(n),
the unitary groups U(n), but mathematicians and physicists are also fascinated by more exotic
examples such as the symmetry group of the octonions which is discussed a lot in modern mathematical
physics. Many of these Lie groups can be represented as subgroups of Gl(k,R) for some sufficiently
large k, but there are also Lie groups which cannot. Lie groups are manifolds G with a group
structure on the underlying set such that the group multiplication is smooth. Lie groups and their
representation is a mighty theory which allows effect calculations both for problems inside
mathematics and also for applications outside (e.g. if in physics or chemistry the coupling of two
electrons with various spin is described, this can be nicely described in terms of representaions of
the Liegroup SU(2)=Spin(3)). This seminar mainly addresses to students in the fifth semesters and
may lead directly to bachelor theses in global analysis. But also other students are very welcome.
The subject fits well with the lecture about Differential Geometry I by Clara Löh: the
contents are almost disjoint but allow many interesting topics for bachelor and master
theses buildung on both courses. If all participants are fluent in German, the seminar will be
held in German, otherwise the English on demand rule of the department will apply.

Literature
A. Knapp, Lie groups beyond an introduction. Birkhäuser 1996. For further literature, refer to
seminar homepage.

Recommended previous knowledge
Analysis I & II, Linear Algebra I & II, Analysis on Manifolds (Analysis IV).

Time/Date
Wednesday 16-18

Location
digital

Course homepage
https://homepages.uni-regensburg.de/~lum63364/LieGroupSeminar/
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Organisational meeting/distribution of topics: Please write one of the organizers to discuss
    which talk you would like to give.
  • Please register via G.R.I.P.S.
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus dem Seminarvortrag
  • Unbenotet:
    • O. g. Studienleistung
Modules
BV, BSem, MV, MSem, LA-GySem

ECTS
Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn
vor WS 15/16