Mathematics Books Algebra BooksLie Algebra Books

Semi Simple Lie Algebras and Their Representations

Semi Simple Lie Algebras and Their Representations

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):

s164 Pages
Similar Books
Introduction to Lie Algebras by J.I. Hall

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

s137 Pages
Introduction to Lie Groups by Alistair Savage

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.

s111 Pages
Lie Groups Representation Theory and Symmetric Spaces

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.

s178 Pages
Lie Algebras and Representation Theory

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.

s102 Pages
Introduction to Lie algebras

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.

sNA Pages
Semi Simple Lie Algebras and Their Representations

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.

s164 Pages
Orbital Integrals on Reductive Lie Groups and Their Algebras

Orbital Integrals on Reductive Lie Groups and Their Algebras

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.

s194 Pages
Matrix Lie Groups And Control Theory

Matrix Lie Groups And Control Theory

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

s60 Pages
Modular Lie Algebras (PDF 74P)

Modular Lie Algebras (PDF 74P)

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 .

s74 Pages
Lie algebras notes (PDF 34P)

Lie algebras notes (PDF 34P)

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.

s34 Pages
Lie algebras by Shlomo Sternberg

Lie algebras by Shlomo Sternberg

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.

s198 Pages
Notes on Lie Algebras

Notes on Lie Algebras

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.

s172 Pages
An Introduction to Lie Groups and Symplectic Geometry

An Introduction to Lie Groups and Symplectic Geometry

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.

s170 Pages
Lie Algebras Lecture               Notes

Lie Algebras Lecture Notes

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.

s34 Pages

Advertisement