

This section contains free ebooks and guides on Lie Algebra, some of the resources in this section can be viewed online and some of them can be downloaded.




Lie groups and Lie algebras by Wilfried SchmidWilfried SchmidPDF  115 Pages  EnglishThis 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.
 Lie Algebras and Representation TheoryAndreas CapPDF  102 Pages  EnglishThe 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.
 Introduction to Lie algebrasProf. Dr. Nicolas PerrinOnline  NA Pages  EnglishIn these lectures we will
start from the beginning the theory of Lie algebras and their representations.
Topics covered includes: General properties of Lie algebras, JordanChevalley
decomposition, semisimple Lie algebras, Classification of complex semisimple Lie
algebras, Cartan subalgebras, classification of connected Coxeter graphs and
complex semisimple Lie algebras, PoicareBirkhoffWitt theorem.
 Introduction to Lie Groups and Lie Algebras Alexander KirillovPDF  177 Pages  EnglishThis 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.
  Semi Simple Lie Algebras and Their RepresentationsRobert
N. CahnPDF  164 Pages  EnglishThe present volume is intended to meet the need of particle physicists
for a book which is accessible to nonmathematicians. The focus is on the
semisimple 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.
 Lecture notes in Lie AlgebrasDavid KazhdanOnline  NA Pages  EnglishThis note covers the following topics:
Universal envelopping algebras, Levi's theorem, Serre's theorem, KacMoody Lie
algebra, The Kostant's form of the envelopping algebra and A beginning of a
proof of the Chevalley's theorem.
 Lie Algebras by Fulton B. GonzalezFulton B. GonzalezPDF  179 Pages  EnglishThis note covers
the following topics: Background Linear Algebra, Lie Algebras: Definition and
Basic Properties, Solvable Lie Algebras and Lie’s Theorem, Nilpotent Lie
Algebras and Engel’s Theorem, Cartan’s Criteria for Solvability and
Semisimplicity, Semisimple Lie Algebras, root Space Decompositions, Classical
Simple Complex Lie Algebras.
 Notes For Lie algebrasKiyoshi IgusaPDF  106 Pages  EnglishThis 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.
 Orbital Integrals on Reductive Lie Groups and Their AlgebrasFrancisco
BulnesPDF  194 Pages  EnglishThis 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.
 Matrix Lie Groups And Control TheoryJimmie LawsonPDF  60 Pages  EnglishThis note covers the
following topics: Matrix and Lie Groups, Dynamics and Control on Matrix Groups,
Optimality and Riccati Equations, Geometric Control.
 Modular Lie Algebras (PDF 74P)Dmitriy RumyninPDF  74 Pages  EnglishThis 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 .
 Lectures on Lie Algebras (PDF 36P)Joseph
BernsteinPDF  36 Pages  EnglishThis 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.
 Lie algebras notes (PDF 34P)Alexei SkorobogatovPDF  34 Pages  EnglishThis 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.
 Theory of representations by Claudio ProcesiNAOnline  NA Pages  EnglishThis
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.
 Lie algebras by Shlomo SternbergShlomo
SternbergPDF  198 Pages  EnglishThis note covers the following topics: The Campbell Baker Hausdorff Formula, sl(2) and its Representations, classical
simple algebra, EngelLieCartanWeyl, 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.
 Notes on Lie AlgebrasHans
SamelsonPDF  172 Pages  EnglishThis 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.
 Notes on Lie GroupsIvan
AvramidiPDF  16 Pages  EnglishThis note covers the following topics: Abstract Group, Continuous Groups, Invariant Subgroups, Homomorphisms, Direct
and Semidirect Products, Group Representations, Multiplevalued
Representations, Universal Covering Group, Matrix Lie Groups, Structure
Constants of a Lie Group, Covering Group.
 An Introduction to Lie Groups and Symplectic GeometryRobert
L. Bryant, Duke University, DurhamPDF  170 Pages  EnglishThe 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.
 Lie methodsArieh
IserlesPDF  148 Pages  EnglishThis note covers the following topics: Numerical analysts in Plato’s
temple, Theory and background, Runge–Kutta on manifolds and RKMK, Magnus and
Fer expansions, Quadrature and graded algebras, Alternative coordinates,
Adjoint methods, Computation of exponentials, Stability and backward error
analysis, Implementation, Applications.
 F. Warner, Foundations of Differentiable Manifolds and Lie Groups (DJVU)  Lie Algebras Lecture NotesAlexei SkorobogatovPDF  34 Pages  EnglishThis 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.
 Lie Algebras by Shlomo SternbergShlomo
SternbergOnline  NA Pages  EnglishThis 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, FriedmannRobertsonWalker metrics in general relativity, Clifford
algebras.
 Expository articles Computing rational points on curves, Elliptic curves 








