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| MATH0469-1 | Differential geometry III
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Lecturer : | Pierre Mathonet |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| In this course, we will essentially study the theory of finite dimensional Lie algebras.
We will focus on classical concepts such as solvable, nilpotent, or semi-simple Lie algebras.
We will also study the representation theory of (semi-simple) Lie algebras and expose the classification of finite dimensional complex simple Lie algebras.
Finally, we will expose a few generalizations of Lie algebras (Lie superalgebras for instance). |
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Learning outcomes of the course :
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| At the end of this lecture series, students should have a good knowledge of Lie algebras. This should help them to read the scientific literature for instance in differential geometry but also in some areas of Physics. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| A good knowledge of linear algebra is necessary. A basic knowledge of differential geometry are necessary is useful. |
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Planned learning activities and teaching methods :
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Mode of delivery (face-to-face ; distance-learning) :
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| The students are supposed to attend the lectures of theory and practice.
The schedule of the lectures and exercise sessions is established by the Department of Mathematics, and is available on its website
http://www.deptmath.ulg.ac.be/
according to the students that have chosen this lecture series before the beginning of the academic year 2012-2013. |
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Recommended or required readings :
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| I can surely recommand the following readings :
W. Fulton and J. Harris : Representation Theory : A first course (Graduate text in Mathematics)
J.E. Humphreys. : Introduction to Lie Algebras and Representation Theory.
Many other textbooks are available at the library (Building B52). |
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Assessment methods and criteria :
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| On oral exam will be organized. The students will be asked to answer questions on some themes studied during the lectures.
They can also be asked to give a presentation on a topic involving the theory developed in the lectures. This topic is determined by the teacher. |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| Feel free to contact me for any question, preferably by e-mail (P.Mathonet@ulg.ac.be) to make an appointment or for very short questions, or come to my office (Building B37, Grande Traverse 12 - Sart Tilman, office 0/27).
You can also try to call me on the
phone 04/366 94 80. |
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