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401-3225-00L  Introduction to Lie Groups

SemesterAutumn Semester 2016
LecturersP. D. Nelson
Periodicityyearly recurring course
Language of instructionEnglish



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: http://www.math.ethz.ch/education/bachelor/lectures/hs2014/math/introlg

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

No public learning materials available.
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-3225-00 GIntroduction to Lie Groups
Lectures take place on Tuesdays (every second week) and on Thursdays (every week).
Exercise sessions take place on Tuesdays (every second week).
4 hrs
Tue/2w10-12HG D 5.2 »
10-12HG D 5.2 »
10-12HG G 26.1 »
Thu10-12HG D 3.2 »
P. D. Nelson

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

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