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Roots of a Compact Lie GroupRoots of a Compact Lie Group
by Kristopher Tapp - arXiv , 2009
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.
(717 views)

Introductory Treatise On Lie's Theory Of Finite Continuous Transformation GroupsIntroductory Treatise On Lie's Theory Of Finite Continuous Transformation Groups
by John Edward Campbell - Oxford Clarendon Press , 1903
In this treatise an attempt is made to give, in as elementary a form as possible, the main outlines of Lie's theory of Continuous Groups. Even those familiar with the theory may find something new in the form in which the theory is here presented.
(545 views)

Lectures on Discrete Subgroups of Lie GroupsLectures on Discrete Subgroups of Lie Groups
by G.D. Mostow - Tata Institute of Fundamental Research , 1969
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.
(1499 views)

Lectures on Lie Groups and Representations of Locally Compact GroupsLectures on Lie Groups and Representations of Locally Compact Groups
by F. Bruhat - Tata Institute of Fundamental Research , 1958
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.
(2621 views)

Lecture Notes in Lie GroupsLecture Notes in Lie Groups
by Vladimir G. Ivancevic, Tijana T. Ivancevic - arXiv , 2011
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.
(2502 views)

Lie GroupsLie Groups
by Robert Gilmore - Drexel University , 2007
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.
(3187 views)

Lie groups and Lie algebrasLie groups and Lie algebras
by N. Reshetikhin, V. Serganova, R. Borcherds - UC Berkeley , 2007
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.
(3818 views)

Introduction to Lie Groups and Lie AlgebrasIntroduction to Lie Groups and Lie Algebras
by Alexander Kirillov, Jr. - SUNY at Stony Brook , 2010
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.
(5232 views)

Algebraic Groups, Lie Groups, and their Arithmetic SubgroupsAlgebraic Groups, Lie Groups, and their Arithmetic Subgroups
by J. S. Milne , 2010
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.
(4345 views)

Notes on Differential Geometry and Lie GroupsNotes on Differential Geometry and Lie Groups
by Jean Gallier - University of Pennsylvania , 2010
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.
(3309 views)

Introduction to Lie Groups, Adjoint Action and Some GeneralizationsIntroduction to Lie Groups, Adjoint Action and Some Generalizations
by Marcos M. Alexandrino, Renato G. Bettiol - arXiv , 2010
These lecture notes provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming at advanced undergraduate and graduate students. A special focus is given to maximal tori and roots of compact Lie groups.
(2992 views)

An Elementary Introduction to Groups and RepresentationsAn Elementary Introduction to Groups and Representations
by Brian C. Hall - arXiv , 2000
An elementary introduction to Lie groups, Lie algebras, and their representations. Topics include definitions and examples of Lie groups and Lie algebras, the basics of representations theory, the Baker-Campbell-Hausdorff formula, and more.
(9259 views)

Lie Groups in PhysicsLie Groups in Physics
by G. 't Hooft, M. J. G. Veltman - Utrecht University , 2007
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.
(6800 views)

Notes on Classical GroupsNotes on Classical Groups
by Peter J. Cameron - Queen Mary and Westfield College , 2000
Notes for an M.Sc. course: Fields and vector spaces; Linear and projective groups; Polarities and forms; Symplectic groups; Unitary groups; Orthogonal groups; Klein correspondence and triality; A short bibliography on classical groups.
(4477 views)

Group Theory: Birdtracks, Lie's, and Exceptional GroupsGroup Theory: Birdtracks, Lie's, and Exceptional Groups
by Predrag Cvitanovic - Princeton University Press , 2008
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.
(6351 views)