The spring semester 2021 will certainly take place online until Easter. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers.

Search result: Catalogue data in Autumn Semester 2016

Mathematics Master Information
Core Courses
For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Core Courses: Pure Mathematics
401-3225-00LIntroduction to Lie GroupsW8 credits4GP. D. Nelson
AbstractTopological 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.
ObjectiveThe 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.
LiteratureA. 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)
Prerequisites / NoticeTopology 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.

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