Lecture Notes on Lie Algebras and Lie Groups

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 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

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

Lecture notes in Lie Algebras

This note covers the following topics: Universal envelopping algebras, Levi's theorem, Serre's theorem, Kac-Moody Lie algebra, The Kostant's form of the envelopping algebra and A beginning of a proof of the Chevalley's theorem.

Author(s): David Kazhdan

NA Pages

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.

Author(s): Kiyoshi Igusa

106 Pages

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.

Author(s): Francisco Bulnes

194 Pages

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 .

Author(s): Dmitriy Rumynin

74 Pages

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.

Author(s): Joseph Bernstein

36 Pages

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.

Author(s): Shlomo Sternberg

198 Pages

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.

Author(s): Robert L. Bryant, Duke University, Durham

170 Pages

Expository articles Computing rational points on curves, Elliptic curves

Currently this section contains no detailed description for the page, will update this page soon.

Author(s): NA

NA Pages