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Differentiable Manifolds and Vector Fields. Definition and Examples Of Lie Groups. Flow On Manifolds, Invariant Vector Fields, One Parameter Subgroups. The Lie Algebra of a Lie Group. The Exponential Map And The Adjoint Respesentation. Homogeneous Spaces, Lie Groups As Symmetr Y Groups. The Fundamental Group of a Lie Group, The Simply Connected Covering Group. Haar Measure.

Faculty: Mathematics
|Undergraduate Studies |Graduate Studies

Pre-required courses

(104004 - Differential and Integral Calculus 2 and 104131 - Ordinary Differential Equations/h and 104134 - Modern Algebra H and 104142 - Int. to Metric and Topological Space) or (104142 - Int. to Metric and Topological Space and 104172 - Introduction to The Theory of Groups and 104281 - Infinitesimal Calculus 2 and 104285 - Ordinary Differential Equations)

• Lie groups : an introduction through linear groups - Rossmann, Wulf
• Lie groups beyond an introduction - Knapp, Anthony W.
• Lie groups beyond an introduction - Knapp, Anthony W.
• Lie Groups Beyond an Introduction [electronic resource] - Knapp, Anthony W.
• Lie groups, Lie algebras, and their representations - Varadarajan, V. S.
• Lie Groups, Lie Algebras, and Their Representations [electronic resource] - Varadarajan, V. S.
• Representations of compact Lie groups - Bröcker, Theodor.
• Representations of Compact Lie Groups [electronic resource] - Bröcker, T.