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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 
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
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
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
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
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
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.
Author(s): Alexei Skorobogatov
34 Pages
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.
Author(s): NA
NA 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
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.
Author(s): Arieh Iserles
148 Pages
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.
Author(s): Alexei Skorobogatov
34 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 PagesAdvertisement
