A Lie algebra is a vector space together with a bilinear operation called the Lie bracket, denoted [-,-]. An example is given by the Lie algebra of n by n matrices over the complex numbers with the Lie bracket defined by [x,y] = xy-yx. Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds, for example the general linear group, or the orthogonal group. Lie algebras appear as 'infinitessimal symmetries' of spaces, which is especially important in physics. The aim in this proseminar is to give an easy introduction to Lie algebras, hopefully getting as far as the classification of complex simple Lie algebras in terms of Dynkin diagrams
Students need a very good understanding of linear algebra, from the courses Linear Algebra I and II.
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24-B-GEO Geometrie (Gym/Ge) | Proseminar | Studienleistung
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Studieninformation |
24-B-PX Praxismodul | Proseminar | Studienleistung
unbenotete Prüfungsleistung |
Studieninformation |
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