Mathematics Books Algebra BooksLie Algebra Books

Lie groups and Lie algebras by Wilfried Schmid

Lie groups and Lie algebras by Wilfried Schmid

Lie groups and Lie algebras by Wilfried Schmid

This note covers the following topics: Geometric preliminaries, The Lie algebra of a Lie group, Lie algebras, Geometry of Lie groups, The Universal Enveloping Algebra, Representations of Lie groups, Compact Lie groups, Root systems, Classificiation of compact Lie groups, Representations of compact Lie groups.

Author(s):

s115 Pages
Similar Books
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
Lecture Notes on Lie Algebras and Lie Groups

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.

s150 Pages
Notes For Lie algebras

Notes For Lie algebras

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.

s106 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
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
Lectures on Lie Algebras (PDF 36P)

Lectures on Lie Algebras (PDF 36P)

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.

s36 Pages
Theory of representations by Claudio Procesi

Theory of representations by Claudio Procesi

This note explains the following topics: Lie groups, Lie algebra associated to a group, Correspondence between groups and algebras, classification of connected compact Lie groups, theory of Cartan Weyl.

sNA 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 methods

Lie methods

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.

s148 Pages
Lie Algebras by Shlomo Sternberg

Lie Algebras by Shlomo Sternberg

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.

sNA Pages

Advertisement