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# Lie Groups

E-Books for free online viewing and/or download

## e-books in this category

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**Roots 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.

(**1012** views)

**Introductory 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.

(**855** views)

**Lectures 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.

(**1840** views)

**Lectures 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.

(**2987** views)

**Lecture 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.

(**2836** views)

**Lie 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.

(**3702** views)

**Lie 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.

(**4271** views)

**Introduction 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.

(**5815** views)

**Algebraic 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.

(**4723** views)

**Notes 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.

(**3706** views)

**Introduction 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.

(**3358** views)

**An 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.

(**9816** views)

**Lie 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.

(**7346** views)

**Notes 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.

(**4835** views)

**Group 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.

(**6905** views)

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