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 F. Bruhat - Tata Institute of Fundamental Research
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.
by G. 't Hooft, M. J. G. Veltman - Utrecht University
Contents: Quantum mechanics and rotation invariance; The group of rotations in three dimensions; More about representations; Ladder operators; The group SU(2); Spin and angular distributions; Isospin; The Hydrogen Atom; The group SU(3); 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 Abraham Cohen - D.C. Heath & co
The object of this book is to present in an elementary manner, in English, an introduction to Lie s theory of one-parameter groups, with special reference to its application to the solution of differential equations invariant under such groups.