Notes on Differential Geometry and Lie Groups
by Jean Gallier
Publisher: University of Pennsylvania 2010
Contents: Introduction to Manifolds and Lie Groups; Review of Groups and Group Actions; Manifolds; Construction of Manifolds From Gluing Data; Lie Groups, Lie Algebra, Exponential Map; The Derivative of exp and Dynkin's Formula; Bundles, Riemannian Metrics, Homogeneous Spaces; Differential Forms; Integration on Manifolds; Distributions and the Frobenius Theorem; Connections and Curvature in Vector Bundles; Geodesics on Riemannian Manifolds; Curvature in Riemannian Manifolds; etc.
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by N. Reshetikhin, V. Serganova, R. Borcherds - UC Berkeley
From the table of contents: Tangent Lie algebras to Lie groups; Simply Connected Lie Groups; Hopf Algebras; PBW Theorem and Deformations; Lie algebra cohomology; Engel's Theorem and Lie's Theorem; Cartan Criterion, Whitehead and Weyl Theorems; etc.
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We consider some heterogeneous topics relating to Lie groups and the general theory of representations of locally compact groups. We have rigidly adhered to the analytic approach in establishing the relations between Lie groups and Lie algebras.