MTL856: Difference between revisions
| [checked revision] | [checked revision] |
Prashantt492 (talk | contribs) Creating course page via bot |
Bot: wrap bare course codes in wikilinks |
||
| Line 5: | Line 5: | ||
| credit_structure = 3-0-0 | | credit_structure = 3-0-0 | ||
| pre_requisites = | | pre_requisites = | ||
| overlaps = MTL756 | | overlaps = [[MTL756]] | ||
}} | }} | ||
== MTL856 : Lie Algebras == | == MTL856 : Lie Algebras == | ||
Definitions and examples. Basic concepts. Solvable and Nilpotent Lie algebras, The Engel's theorem, Lie's theorem, Cartan's criterion, Killing form, Finite dimensional semi-simple Lie algebras and their representation theory. The Weyl's theorem. Representations of sl (2,C). Root space decomposition. Rationality properties. Root systems, The Weyl group. Isomorphism and conjugacy theorems (Cartan subalgebras, Borel subalgebras). Universal enveloping algebras, PBW theorem, Serre's theorem. Representation theory and characters. Formulas of Weyl, Kostant and Steinberg. Introduction to infinite dimensional Lie algebras. | Definitions and examples. Basic concepts. Solvable and Nilpotent Lie algebras, The Engel's theorem, Lie's theorem, Cartan's criterion, Killing form, Finite dimensional semi-simple Lie algebras and their representation theory. The Weyl's theorem. Representations of sl (2,C). Root space decomposition. Rationality properties. Root systems, The Weyl group. Isomorphism and conjugacy theorems (Cartan subalgebras, Borel subalgebras). Universal enveloping algebras, PBW theorem, Serre's theorem. Representation theory and characters. Formulas of Weyl, Kostant and Steinberg. Introduction to infinite dimensional Lie algebras. | ||
Latest revision as of 16:43, 14 April 2026
| MTL856 | |
|---|---|
| Lie Algebras | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | |
| Overlaps | MTL756 |
MTL856 : Lie Algebras
Definitions and examples. Basic concepts. Solvable and Nilpotent Lie algebras, The Engel's theorem, Lie's theorem, Cartan's criterion, Killing form, Finite dimensional semi-simple Lie algebras and their representation theory. The Weyl's theorem. Representations of sl (2,C). Root space decomposition. Rationality properties. Root systems, The Weyl group. Isomorphism and conjugacy theorems (Cartan subalgebras, Borel subalgebras). Universal enveloping algebras, PBW theorem, Serre's theorem. Representation theory and characters. Formulas of Weyl, Kostant and Steinberg. Introduction to infinite dimensional Lie algebras.