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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 
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 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
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.
Author(s): Prof. Dr. Nicolas Perrin
NA 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
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
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.
Author(s): Jimmie Lawson
60 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
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
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.
Author(s): Hans Samelson
172 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
F. Warner, Foundations of Differentiable Manifolds and Lie Groups (DJVU)
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
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.
Author(s): Shlomo Sternberg
NA PagesAdvertisement
