Login for PhD students/staff at UCPH      Login for others
Introduction to Lie Algebras
Provider: Faculty of Science

Activity no.: 5566-20-07-31 
Enrollment deadline: 03/02/2020
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time03.02.2020, at: 09:00 - 03.04.2020, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserBergfinnur Durhuus    E-mail address: durhuus@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 3
Scheme groupC
Exam formContinuous assessment
Exam formContinuous assessment
Exam detailsTwo longer written assignments in week 5 and week 9, plus 5 smaller written assignments in weeks 2,3,4,6,7. The assignments will be graded on a scale from 0 to 100% and in order to pass the student must obtain at least 50% for each assignment. All aids allowed
Course workload
Course workload categoryHours
Lectures32.00
Theory exercises32.00
Preparation122.00
Exam20.00
Sum206.00
Content
1) Lie algebras

2) Matrix Lie algebras

3) Some representation theory

4) Structure theory of Lie algebras

5) Cartan-Weyl basis

6) Classification of simple Lie algebras

Learning outcome
At the end of the course the students are expected to have acquired the following knowledge and associated tool box:
- the mathematical framework of Lie algebras, including basic examples in the form of matrix Lie algebras
- basic representation theory of Lie algebras
- structure theory of Lie algebras, with main emphasis on semi-simple Lie algebras
- Killing form, roots, and root space decomposition
- the fundamental classification theorems for simple Lie algebras, including Serre's theorem

Skills:
- be able to use the fundamental results on Lie algebras to solve concrete mathematical problems
- be able to work rigorously with representaions of Lie algebras, including decompositions in special cases
- be able to formulate and solve certain types of physical problems by applying the theory of Lie algebras and their representations

Competences: The course aims at training the students in formulating and handling specific mathematical problems, possibly inspired by physics, by use of the theory of Lie algebras and their representations.

Literature
Lecture notes will be made available through Absalon.

Teaching and learning methods
8 weeks with 2x2 lectures and 2x2 exercise sessions per week.

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.