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 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.
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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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.
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'Continuous Groups Of Transformations' sets forth the general theory of Lie and his contemporaries and the results of recent investigations with the aid of the methods of the tensor calculus and concepts of the new differential geometry.