MTL756: Difference between revisions
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| credits = 3 | | credits = 3 | ||
| credit_structure = 3-0-0 | | credit_structure = 3-0-0 | ||
| pre_requisites = MTL105/MTL501 | | pre_requisites = [[MTL105]]/[[MTL501]] | ||
| overlaps = MTL856 | | overlaps = [[MTL856]] | ||
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== MTL756 : Lie Algebras and Lie Groups == | == MTL756 : Lie Algebras and Lie Groups == | ||
Definition and examples, solvable and nilpotent Lie algebras, the Engel's theorem, Lie's theorem, Cartan's theorem, killing form. Representation theory of finite dimensional semisimple Lie algebras. The Weyl's theorem, representations of sl(2,C), root space decomposition. Weyl group, Cartan subalgebras and classification of root systems; Definition and examples of matrix Lie groups. Exponential mapping, Baker-Campbell-Hausdorff formula. Representation theory of matrix Lie groups. Representation theory of SU(2) and SU(3). | Definition and examples, solvable and nilpotent Lie algebras, the Engel's theorem, Lie's theorem, Cartan's theorem, killing form. Representation theory of finite dimensional semisimple Lie algebras. The Weyl's theorem, representations of sl(2,C), root space decomposition. Weyl group, Cartan subalgebras and classification of root systems; Definition and examples of matrix Lie groups. Exponential mapping, Baker-Campbell-Hausdorff formula. Representation theory of matrix Lie groups. Representation theory of SU(2) and SU(3). | ||
Latest revision as of 16:43, 14 April 2026
| MTL756 | |
|---|---|
| Lie Algebras and Lie Groups | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | MTL105/MTL501 |
| Overlaps | MTL856 |
MTL756 : Lie Algebras and Lie Groups
Definition and examples, solvable and nilpotent Lie algebras, the Engel's theorem, Lie's theorem, Cartan's theorem, killing form. Representation theory of finite dimensional semisimple Lie algebras. The Weyl's theorem, representations of sl(2,C), root space decomposition. Weyl group, Cartan subalgebras and classification of root systems; Definition and examples of matrix Lie groups. Exponential mapping, Baker-Campbell-Hausdorff formula. Representation theory of matrix Lie groups. Representation theory of SU(2) and SU(3).