Lie algebras
by Wan, Zhexian
Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of…
Read More ↓Title Statements
- Full title :Lie algebras / by Zhe-Xian Wan ; translated by Che-Young Lee.
Summary
Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra.
Read More ↓Edition Statements
- Publication Date:1975
- Edition:First edition]
Publication Statements
- Publisher(s):Pergamon Press
- Place of Publication:Oxford
- Language:eng
- Publication Date:1975
Notes
Translation of: Li daishu.
Includes index.
The Physical Object
- Description:1 online resource (vii, 230 pages)
Edition Identifiers
- ISBN:9781483187303, 1483187306
- oclc:ocn893872963
- LC Classification:QA252.3
- Dewey Decimal:512/.55
Table of Contents
Front Cover; Lie Algebras; Copyright Page; Table of Contents; PREFACE; CHAPTER 1. BASIC CONCEPTS; 1.1. Lie algebras; 1.2. Subalgebras, ideals and quotient algebras; 1.3. Simple algebras; 1.4. Direct sum; 1.5. Derived series and descending central series; 1.6. Killing form; CHAPTER 2. NILPOTENT AND SOLVABLE LIE ALGEBRAS; 2.1. Preliminaries; 2.2. Engel's theorem; 2.3. Lie's theorem; 2.4. Nilpotent linear Lie algebras; CHAPTER 3. CARTAN SUBALGEBRAS; 3.1. Cartan subalgebras; 3.2. Existence of Cartan subalgebras; 3.3. Preliminaries; 3.4. Conjugacy of Cartan subalgebras.
CHAPTER 4. CARTAN'S CRITERION4.1. Preliminaries; 4.2. Cartan's criterion for solvable Lie algebras; 4.3. Cartan's criterion for semisimple Lie algebras; CHAPTER 5. CARTAN DECOMPOSITIONS AND ROOT SYSTEMS OF SEMISIMPLE LIE ALGEBRAS; 5.1. Cartan decompositions of semisimple Lie algebras; 5.2. Root systems of semisimple Lie algebras; 5.3. Dependence of structure of semisimple Lie algebras on root systems; 5.4. Root systems of the classical Lie algebras; CHAPTER 6. FUNDAMENTAL SYSTEMS OF ROOTS OF SEMISIMPLE LIE ALGEBRAS AND WEYL GROUPS; 6.1. Fundamental systems of roots and prime roots.
9.3. Representations of the three-di…
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