Notes on Classical Groups
by Peter J. Cameron
Publisher: Queen Mary and Westfield College 2000
Number of pages: 96
These notes are the content of an M.Sc. course the author gave at Queen Mary and Westfield College, London. Contents: Fields and vector spaces; Linear and projective groups; Polarities and forms; Symplectic groups; Unitary groups; Orthogonal groups; Klein correspondence and triality; A short bibliography on classical groups.
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by Jean Gallier - University of Pennsylvania
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; etc.
by E. Celledoni, H. Marthinsen, B. Owren - arXiv
The authors give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented ...
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 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.