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.
Home page url
Download or read it online for free here:
(multiple PDF files)
by G.D. Mostow - Tata Institute of Fundamental Research
Contents: Preliminaries; Complexification of a real Linear Lie Group; Intrinsic characterization of K* and E; R-regular elements; Discrete Subgroups; Some Ergodic Properties of Discrete Subgroups; Real Forms of Semi-simple Algebraic Groups; etc.
by Kristopher Tapp - arXiv
This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary abstractions.
by J. S. Milne
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.
by Predrag Cvitanovic - Princeton University Press
A book on the theory of Lie groups for researchers and graduate students in theoretical physics and mathematics. It answers what Lie groups preserve trilinear, quadrilinear, and higher order invariants. Written in a lively and personable style.