Introduction To Lie Algebras And Representation Theory




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Course Contents

Definitions and first examples. Classical Lie algebras. Ideals and homo-morphisms. Niporent Lie algebras. Engel's theorem. Solvable Lie algebras. Lie's theorem. Jordan Chevalley Decomposition. Radical and semi simplicity. The Killing form and Cartan's criterion. THe structure of semi simple Lie algebras. Complete reducibility and Weyls theorem. Representation theory of the Lie algebra sl (2). Total sub algebras and root systems. Integrality properties. Simple Lie algebras and irreducible root systems. 



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