Mathematics Books Algebra BooksLie Algebra Books

Introduction to Lie Groups by Alistair Savage

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.

Author(s):

s111 Pages
Similar Books
Introduction to Lie Algebras by J.I. Hall

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

s137 Pages
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
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
Matrix Lie Groups And Control Theory

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.

s60 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
Lie algebras notes (PDF 34P)

Lie algebras notes (PDF 34P)

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.

s34 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
Lie algebras by Shlomo Sternberg

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.

s198 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
Expository articles   Computing rational points on curves, Elliptic curves

Expository articles Computing rational points on curves, Elliptic curves

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

sNA Pages

Advertisement