401-3225-00L  Introduction to Lie Groups

SemesterAutumn Semester 2021
LecturersA. Iozzi
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3225-00 GIntroduction to Lie Groups
Groups are selected in myStudies.
4 hrs
Wed08:15-10:00ML E 12 »
Thu10:15-12:00LFO C 13 »
A. Iozzi

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: Link

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits8 credits
ExaminersA. Iozzi
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

 
Main linkInformation
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Groups

401-3225-00 GIntroduction to Lie Groups
GroupG
Wed08:15-10:00ML E 12 »
Thu10:15-12:00LFO C 13 »

Restrictions

There are no additional restrictions for the registration.

Offered in

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