MATH-M 507: INTRODUCTION TO LIE ALGEBRAS AND LIE GROUPS (3 credits)

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Nilpotent, solvable, and semisimple Lie algebras, exponential map, PBW theorem, Killing form, Cartan subalgebras, root systems, Weyl group, classification and representations of complex semisimple Lie algebras, Schur's lemma, maximal weight modules; correspondence between real Lie algebras and Lie groups, compact Lie groups, complex and real semisimple Lie groups, symmetric spaces.

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