Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
Introduction to Lie algebras
In these lectures we will start from the beginning the theory of Lie algebras and their representations. Topics covered includes: General properties of Lie algebras, Jordan-Chevalley decomposition, semisimple Lie algebras, Classification of complex semisimple Lie algebras, Cartan subalgebras, classification of connected Coxeter graphs and complex semisimple Lie algebras, Poicare-Birkhoff-Witt theorem.
Author(s): Prof. Dr. Nicolas Perrin
NA Pages 
Lie algebras and representation theory by Dietrich Burde
This note covers basic notions of lie algebra theory, Structure theory of lie algebras, Representations of semi simple lie algebras.
Author(s): Dietrich Burde
113 Pages
Lie Algebras and Their Representations
This note explains the following topics: Representations of sl2, Structure and classification of simple lie algebras, Structure theory of semisimple lie algebras and root systems.
Author(s): University of Cambridge
34 Pages
Introduction to Lie Algebras by J.I. Hall
The primary aim of this note is the introduction and discussion of the finite dimensional semisimple Lie algebras over algebraically closed fields of characteristic and their representations. Topics covered includes: Types of algebras, Jordan algebras, Lie algebras and representation, Matrix algebras, Lie groups, Basic structure theory and Basic representation theory, Nilpotent representations, Killing forms and semisimple Lie algebras, Semisimple Lie algebras, Representations of semisimple algebras
Author(s): J.I. Hall
137 Pages
Introduction to Lie Groups by Alistair Savage
This note focus on the so-called matrix Lie groups since this allows us to cover the most common examples of Lie groups in the most direct manner and with the minimum amount of background knowledge. Topics covered includes: Matrix Lie groups, Topology of Lie groups, Maximal tori and centres, Lie algebras and the exponential map, Covering groups.
Author(s): Alistair Savage
111 Pages
Lie Groups Representation Theory and Symmetric Spaces
This note covers the following topics: Fundamentals of Lie Groups, A Potpourri of Examples, Basic Structure Theorems, Complex Semisimple Lie algebras, Representation Theory, Symmetric Spaces.
Author(s): Wolfgang Ziller
178 Pages
Lie Algebras and Representation Theory
The aim of this note is to develop the basic general theory of Lie algebras to give a first insight into the basics of the structure theory and representation theory of semi simple Lie algebras. Topics covered includes: Group actions and group representations, General theory of Lie algebras, Structure theory of complex semisimple Lie algebras, Cartan subalgebras, Representation theory of complex semisimple Lie algebras, Tools for dealing with finite dimensional representations.
Author(s): Andreas Cap
102 Pages
In these lectures we will start from the beginning the theory of Lie algebras and their representations. Topics covered includes: General properties of Lie algebras, Jordan-Chevalley decomposition, semisimple Lie algebras, Classification of complex semisimple Lie algebras, Cartan subalgebras, classification of connected Coxeter graphs and complex semisimple Lie algebras, Poicare-Birkhoff-Witt theorem.
Author(s): Prof. Dr. Nicolas Perrin
NA Pages
Introduction to Lie Groups and Lie Algebras
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.
Author(s): Alexander Kirillov
177 Pages