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FSF3604 Lie Algebras 7.5 credits

Information per course offering

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Course syllabus as PDF

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Course syllabus FSF3604 (Spring 2019–)
Headings with content from the Course syllabus FSF3604 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Definition of Lie algebras, small-dimensional examples, some classical groups and their Lie algebras (treated informally). Ideals, subalgebras, homomorphisms, modules. Nilpotent algebras, Engel's theorem; soluble algebras, Lie's theorem. Semisimple algebras and Killing form, Cartan's criteria for solubility and semisimplicity, Weyl's theorem on complete reducibility of representations of semisimple Lie algebras. The root space decomposition of a Lie algebra; root systems, Cartan matrices and Dynkin diagrams. Discussion of classification of irreducible root systems, and semisimple Lie algebras.

Intended learning outcomes

Students will learn how to utilise various techniques for working with Lie algebras, and they will gain an understanding of parts of a major classification result.

Literature and preparations

Specific prerequisites

Master's or Master's degree with at least 30 credits in mathematics.

Suitable prerequisites are courses in differential geometry and representation theory. Very good knowledge of linear algebra.

Literature

Brian C. Hall, "Lie Groups, Lie Algebras, and Representations: An Elementary Introduction "(Graduate Texts in Mathematics) 2nd ed. 2015 Edition.

See http://www.amazon.com/Lie-Groups-Algebras-Representations-Introduction/dp/3319134663/ref=sr_1_1?ie=UTF8&qid=1460893363&sr=8-1&keywords=lie+groups+hall

Examination and completion

Grading scale

G

Examination

  • SEM1 - Seminars, 7.5 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

If the course is discontinued, students may request to be examined during the following two academic years.

Oral examination

Other requirements for final grade

Continuous oral examination

Examiner

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Education cycle

Third cycle

Postgraduate course

Postgraduate courses at SCI/Mathematics