Roots of a Compact Lie Group
by Kristopher Tapp
Publisher: arXiv 2009
Number of pages: 39
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. Some familiarity with matrix groups and with maximal tori is assumed.
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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 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 Robert Gilmore - Drexel University
The book emphasizes the most useful aspects of Lie groups, in a way that is easy for students to acquire and to assimilate. It includes a chapter dedicated to the applications of Lie group theory to solving differential equations.
by Predrag Cvitanovic - Princeton University Press
A book on the theory of Lie groups for researchers and graduate students in theoretical physics and mathematics. It answers what Lie groups preserve trilinear, quadrilinear, and higher order invariants. Written in a lively and personable style.