Introduction to Lie Groups and Lie Algebras

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

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

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

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