Overview

This revised edition of Notes on Lie Algebras covers structuring, classification, and representations of semisimple Lie algebras, a classical field that has become increasingly important to mathematicians and physicists. The text's purpose is to introduce the student to the basic facts and their derivations using a direct approach in today's style of thinking and language. The main prerequisite for a clear understanding of the book is Linear Algebra, of a reasonably sophisticated nature. For this revised edition, errors have been eliminated, a number of proofs have been rewritten with more clarity, and some new material has been added.

Full Product Details

Author:   Hans Samelson ,  Hans Samelson
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Second Edition 1990
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.277kg
ISBN:  

9780387972640

ISBN 10:   0387972641
Pages:   163
Publication Date:   01 June 1990
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Generalities.- 1.1 Basic definitions, examples.- 1.2 Structure constants.- 1.3 Relations with Lie groups.- 1.4 Elementary algebraic concepts.- 1.5 Representations; the Killing form.- 1.6 Solvable and nilpotent.- 1.7 Engel’s theorem.- 1.8 Lie’s theorem.- 1.9 Cartan’s first criterion.- 1.10 Cartan’s second criterion.- 1.11 Representations of A1.- 1.12 Complete reduction for A1.- 2 Structure Theory.- 2.1 Cartan subalgebra.- 2.2 Roots.- 2.3 Roots for semisimple g.- 2.4 Strings.- 2.5 Cartan integers.- 2.6 Root systems, Weyl group.- 2.7 Root systems of rank two.- 2.8 Weyl-Chevalley normal form, first stage.- 2.9 Weyl-Chevalley normal form.- 2.10 Compact form.- 2.11 Properties of root systems.- 2.12 Fundamental systems.- 2.13 Classification of fundamental systems.- 2.14 The simple Lie algebras.- 2.15 Automorphisms.- 3 Representations.- 3.1 The Cartan-Stiefel diagram.- 3.2 Weights and weight vectors.- 3.3 Uniqueness and existence.- 3.4 Complete reduction.- 3.5 Cartan semigroup; representation ring.- 3.6 The simple Lie algebras.- 3.7 The Weyl character formula.- 3.8 Some consequences of the character formula.- 3.9 Examples.- 3.10 The character ring.- 3.11 Orthogonal and symplectic representations.- References.- Symbol Index.

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