401-3225-00L  Introduction to Lie Groups

SemesterAutumn Semester 2019
LecturersP. D. Nelson
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3225-00 GIntroduction to Lie Groups
Lectures take place on Tuesdays (every week) and on Thursdays (every second week).
Exercise sessions take place on Thursdays (every second week).
4 hrs
Tue10-12HG D 3.2 »
Thu/2w08-10HG D 3.2 »
08-10HG D 3.2 »
P. D. Nelson

Catalogue data

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.

Course webpage: https://metaphor.ethz.ch/x/2018/hs/401-3225-00L/

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits8 credits
ExaminersP. D. Nelson
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
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Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterCore Courses: Pure MathematicsWInformation