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 Alexander Kirillov, Jr. - SUNY at Stony Brook
The book covers the basic contemporary theory of Lie groups and Lie algebras. This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style.
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 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.
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.