Vorlesung

Lokally Compact Groups

Wintersemester 2024/25

Prof.Dr. Linus Kramer

mit Raquel Murat García

Course Locally Compact Groups
Locally compact groups are topological groups which play a role in different areas of mathematics such as geometry, geometric group theory, Lie theory, operator theory or harmonic analysis. We first study general topics in topological groups like subgroups, quotients, connectedness, and actions. Then we consider profinite groups and van Dantzig's theorem. After this we turn to the more advanced structure theory. We will introduce the Haar integral and use it to prove the Peter-Weyl theorem about the structure of compact groups. In the last part of the course we will consider Pontrjagin-Van Kampen duality of compact and locally compact abelian groups.

Audience: The course is aimed at advanced BSC students and MSC students. The topic is well suitable for a master's thesis (or a bachlor's thesis).

Prerequisites: Basic algebra (groups, rings, vector spaces and modules) and point-set topology (as covered in the course Grundlagen der Analysis, Topologie und Geometrie). Knowledge about Lie groups or functional analysis are certainly helpful, but not required for this course.

Die Vorlesung findet Dienstag und Freitag 8:15 - 10:00 Uhr im M4 statt. Sie beginnt am Di 8.10.2017 um 8:15 Uhr.

Literature

Außenhofer, Dikranjan, Giordano Bruno, Topological groups and the Pontryagin-van Kampen duality
Deitmar, Echterhoff, Principles of harmonic analysis
Dugundji, Topology
Hewitt, Ross, Abstract harmonic analysis I
Hofmann, Morris, The structure of compact groups
Hofmann, Morris, The Lie theory of connected pro-Lie groups
Stroppel, Locally compact groups
Wilson, Profinite groups