Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Lie Groups (GeomLie)

Practical information
Study year 2016/2017
Time
Block 4
Programme level Full Degree Master
ECTS 7,5 ECTS
Course responsible
  • Hans Plesner Jakobsen (8-71687276697a6c754774687b6f35727c356b72)
Phone +45 35 32 06 89, room 04.4.15
  • Department of Mathematical Sciences
Course number: NMAK13013U

Course content

(A) Lie groups and Lie algebras; definitions and examples.
(B) Invariant vector fields and the exponential map.
(C) The Lie algebra of a Lie group, Ad and ad.
(D) Homomorphisms, subgroups, sub¬algebras.
(E) Fibre bundles and homogeneous spaces.
(F) Representationsof sl(2,C)
(G) Roots and weights
(H) Root systems and their classification

Learning outcome

Knowledge: basic definitions, examples and theorems of the theory
Skill: ability to use the above
Competence: perform logic reasoning within the theory

Recommended prerequisites

Geometri 2 (Geom2) or similar.

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Education

MSc Programme in Mathematics

Studyboard

Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

A
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Teaching and learning methods

5 hours of lectures and 2 hours of exercises per week for 9 weeks.

Capacity

No limit

Language

English

Workload

Category Hours
Lectures 45
Theory exercises 18
Preparation 143
English 206

Exam

Type of assessment

Continuous assessment
3 mandatory homework assignments to be returned in weeks 5, 7 and 9 of the course. The assignments counts equally towards the grade.

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Censorship form

No external censorship
One internal examiner.

Re-exam

A 30 minutes oral examination without preparation time. No aids. Several internal examiners

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