Mathematik - WiSe 2020/21

-Diese Plattform wird ausschließlich zur Abgabe der Übungsblätter, und Erhlalt deren Korrektur verwendet. 

-Ihr habt jeweils spätestens bis Donnerstags um 10:15 Uhr Zeit eure Lösungen als "PDF Dokument" hochzuladen. 

-Gruppenarbeit ist zugelassen. Bei einer Gruppenarbeit reicht es aus wenn nur ein Person die Lösungen im Namen der Gruppe hochlädt, allerdings die Namen von allen Gruppenmitglieder sollten im Dateinamen des PDF-Dokumentes erwähnt sein. 

-Die Übungsblätter werden Wochenlicht in der Kurswebseite veröffentlicht.

A Lie group is a group which is also a smooth manifold, in way that the group multiplication and the inversion are smooth maps. Examples of Lie groups are matrix groups like the linear group GL(n,R) or the orthogonal group O(n). Lie groups play an important role in many parts of mathematics and physics. They almost inevitably occur when a problem or configuration is invariant under symmetries.

In the lecture we will discuss structural results about Lie groups as well as examples and applications. An important tool will be the Lie functor, which assigns to every Lie group its so-called Lie algebra. The Lie algebra is an infinitesimal version of the Lie group that encodes surprisingly much information about it, and that can be well studied via methods from linear algebra. This will allow us to establish a classification of complex semi-simple Lie algebras and of compact Lie groups. In doing so we will argue from a geometric perspective whenever possible. In particular, we will follow an approach suggested by Cartan that is more geometric than the standard one.