Introduction to Lie Groups, Adjoint Action and Some Generalizations
by Marcos M. Alexandrino, Renato G. Bettiol
Publisher: arXiv 2010
Number of pages: 129
The main purpose of these lecture notes is to provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming mostly at advanced undergraduate and graduate students. A special focus is given to maximal tori and roots of compact Lie groups, exploring its connection with isoparametric submanifolds and polar actions.
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by Vladimir G. Ivancevic, Tijana T. Ivancevic - arXiv
These notes are designed for a 1-semester third year or graduate course in mathematics, physics, or biology. We give both physical and medical examples of Lie groups. The only necessary background are advanced calculus and linear algebra.
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.
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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 ...