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This section contains free e-books and guides on Lie Algebra, some of the resources in this section can be viewed online and some of them can be downloaded.

Lie Algebra Books
Online Books
Introduction to Lie Groups and Lie Algebras

PDF | 177 Pages | English
This book covers the following topics: Lie Groups:Basic Definitions, Lie algebras, Representations of Lie Groups and Lie Algebras, Structure Theory of Lie Algebras, Complex Semisimple Lie Algebras, Root Systems, Representations of Semisimple Lie Algebras, Root Systems and Simple Lie Algebras.

 
Lecture Notes on Lie Algebras and Lie Groups

PDF | 150 Pages | English
This book covers the following topics: Elements of Group Theory, Lie Groups and Lie Algebras, Representation theory.

 
Semi Simple Lie Algebras and Their Representations

PDF | 164 Pages | English
The present volume is intended to meet the need of particle physicists for a book which is accessible to non-mathematicians. The focus is on the semi-simple Lie algebras, and especially on their representations since it is they, and not just the algebras themselves, which are of greatest interest to the physicist. Topics covered includes:The Killing Form, The Structure of Simple Lie Algebras, A Little about Representations, Structure of Simple Lie Algebras, Simple Roots and the Cartan Matrix, The Classical Lie Algebras, The Exceptional Lie Algebras, Casimir Operators and Freudenthal’s Formula, The Weyl Group, Weyl’s Dimension Formula, Reducing Product Representations, Subalgebras and Branching Rules.

 
Lecture notes in Lie Algebras

Online | NA Pages | English
This note covers the following topics: Universal envelopping algebras, Levi's theorem, Serre's theorem, Kac-Moody Lie algebra, The Kostant's form of the envelopping algebra and A beginning of a proof of the Chevalley's theorem.

 
Lie Algebras by Fulton B. Gonzalez

PDF | 179 Pages | English
This note covers the following topics: Background Linear Algebra, Lie Algebras: Definition and Basic Properties, Solvable Lie Algebras and Lie’s Theorem, Nilpotent Lie Algebras and Engel’s Theorem, Cartan’s Criteria for Solvability and Semisimplicity, Semisimple Lie Algebras, root Space Decompositions, Classical Simple Complex Lie Algebras.

 
Notes For Lie algebras

PDF | 106 Pages | English
This note covers the following topics: Ideals and homomorphism, Nilpotent and solvable Lie algebras , Jordan decomposition and Cartan's criterion, Semisimple Lie algebras and the Killing form, Abstract root systems, Weyl group and Weyl chambers, Classification of semisimple Lie algebras , Exceptional Lie algebras and automorphisms, Isomorphism Theorem, Conjugacy theorem.

 
Orbital Integrals on Reductive Lie Groups and Their Algebras

PDF | 194 Pages | English
This is an open source book written by Francisco Bulnes. The purpose of this book is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.

 
Matrix Lie Groups And Control Theory

PDF | 60 Pages | English
This note covers the following topics: Matrix and Lie Groups, Dynamics and Control on Matrix Groups, Optimality and Riccati Equations, Geometric Control.

 
Notes Lie Groups and Lie Algebras

PDF | 134 Pages | English
This note covers the following topics: Motivation: Closed Linear Groups, Differential Geometry, General theory of Lie groups, General theory of Lie algebras, Classi cation of Semisimple Lie Algebras and Representation Theory of Semisimple Lie Groups.

 
Modular Lie Algebras (PDF 74P)

PDF | 74 Pages | English
This note covers the following topics: Free algebras, Universal enveloping algebras , p th powers, Uniqueness of restricted structures, Existence of restricted structures , Schemes, Differential geometry of schemes, Generalised Witt algebra, Filtrations, Witt algebras are generalised Witt algebra, Differentials on a scheme, Lie algebras of Cartan type, Root systems, Chevalley theorem, Chevalley reduction, Simplicity of Chevalley reduction, Chevalley groups,  Abstract Chevalley groups, Engel Lie algebras and Lie algebra associated to a group .

 
Lectures on Lie Algebras (PDF 36P)

PDF | 36 Pages | English
This is a lecture note for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations to derive the Weyl character formula.

 
Lie algebras notes (PDF 34P)

PDF | 34 Pages | English
This note explains the following topics: Basic definitions and examples, Theorems of Engel and Lie, The Killing form and Cartan’s criteria, Cartan subalgebras, Semisimple Lie algebras, Root systems, Classification and examples of semisimple Lie algebras.

 
Lie algebras by Shlomo Sternberg

PDF | 198 Pages | English
This note covers the following topics: The Campbell Baker Hausdorff Formula, sl(2) and its Representations, classical simple algebra, Engel-Lie-Cartan-Weyl, Conjugacy of Cartan sub algebras, simple finite dimensional algebras, Cyclic highest weight modules, Serre’s theorem, Clifford algebras and spin representations, The Kostant Dirac operator.

 
Notes on Lie Algebras

PDF | 172 Pages | English
This book presents a simple straightforward introduction, for the general mathematical reader, to the theory of Lie algebras, specifically to the structure and the (finite dimensional) representations of the semisimple Lie algebras.

 
Notes on Lie Groups

PDF | 16 Pages | English
This note covers the following topics: Abstract Group, Continuous Groups, Invariant Subgroups, Homomorphisms, Direct and Semi-direct Products, Group Representations, Multiple-valued Representations, Universal Covering Group, Matrix Lie Groups, Structure Constants of a Lie Group, Covering Group.

 
An Introduction to Lie Groups and Symplectic Geometry

PDF | 170 Pages | English
The course note really was designed to be an introduction, aimed at an audience of students who were familiar with basic constructions in differential topology and rudimentary differential geometry, who wanted to get a feel for Lie groups and symplectic geometry.

 
Lie methods

PDF | 148 Pages | English
This note covers the following topics: Numerical analysts in Plato’s temple, Theory and background, Runge–Kutta on manifolds and RK-MK, Magnus and Fer expansions, Quadrature and graded algebras, Alternative coordinates, Adjoint methods, Computation of exponentials, Stability and backward error analysis, Implementation, Applications.

 
F. Warner, Foundations of Differentiable Manifolds and Lie Groups (DJVU)
Lie Algebras Lecture Notes

PDF | 34 Pages | English
This note covers the following topics: Basic definitions and examples, Theorems of Engel and Lie, The Killing form and Cartan’s criteria, Cartan subalgebras, Semisimple Lie algebras, Root systems, Classification and examples of semisimple Lie algebras.

 
Lie Algebras by Shlomo Sternberg

Online | NA Pages | English
This note covers the following topics: Applications of the Cartan calculus, category of split orthogonal vector spaces, Super Poison algebras and Gerstenhaber algebras, Lie groupoids and Lie algebroids, Friedmann-Robertson-Walker metrics in general relativity, Clifford algebras.

 
Expository articles Computing rational points on curves, Elliptic curves
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