Suchergebnis: Katalogdaten im Herbstsemester 2016
Mathematik Master | ||||||
Kernfächer Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen. | ||||||
Kernfächer aus Bereichen der reinen Mathematik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|
401-3225-00L | Introduction to Lie Groups | W | 8 KP | 4G | P. D. Nelson | |
Kurzbeschreibung | Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. | |||||
Lernziel | The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. | |||||
Literatur | A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A.Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F.Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S.Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A.Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press) | |||||
Voraussetzungen / Besonderes | Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. Course webpage: Link |
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