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Semi Simple Lie Algebras and Their Representations
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.
Author(s): Robert N. Cahn
164 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
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
Lie Algebras by Brooks Roberts
This note covers the following topics: Solvable and nilpotent Lie algebras, The theorems of Engel and Lie, representation theory, Cartan’s criteria, Weyl’s theorem, Root systems, Cartan matrices and Dynkin diagrams, The classical Lie algebras, Representation theory.
Author(s): Brooks Roberts
217 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
Lecture Notes on Lie Algebras and Lie Groups
This book covers the following topics: Elements of Group Theory, Lie Groups and Lie Algebras, Representation theory.
Author(s): Luiz Agostinho Ferreira
150 Pages