Advertisement

© 2005

Lie Algebras and Algebraic Groups

Benefits

  • Devoted to the theory of Lie algebras and algebraic groups

  • Includes a considerable amount of commutative algebra and algebraic geometry so as to make the book as self-contained as possible

  • Includes all the material required (basic and advanced) for studying the theory of Lie algebras and algebraic groups

  • Includes detailed proofs

  • Moreover, also includes some new and unpublished results

Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Pages 11-29
  3. Pages 31-37
  4. Pages 39-53
  5. Pages 55-73
  6. Pages 95-101
  7. Pages 103-112
  8. Pages 131-145
  9. Pages 167-182
  10. Pages 183-190
  11. Pages 191-204
  12. Pages 205-218
  13. Pages 219-232
  14. Pages 233-275
  15. Pages 277-297

About this book

Introduction

The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.

Keywords

Abstract algebra Algebra Algebraic geometry Algebraic groups Commutative algebra algebra algebras Zariski topology algebraic varieties

Authors and affiliations

  1. 1.Département de MathématiquesUniversité de Poitiers, Boulevard Marie et Pierre CurieFuturoscope Chasseneuil cedexFrance

Bibliographic information

Reviews

From the reviews:

"As Tauvel and Yu focus on algebraic groups, they approach Lie theory via algebraic geometry and even develop that subject from scratch … . For the purpose at hand, Tauvel and Yu’s work compares favorably … . Summing Up: Highly recommended. Upper-division undergraduates through professionals." (D.V. Feldman, Choice, 43:10, June 2006)

"The sheer volume of material covered herein should make this book an invaluable reference for people interested in, or teaching, Lie algebras or algebraic groups. It truly provides ‘one stop shopping’ for someone needing a result or hard-to-find proof. … I cannot even begin to imagine how much work must have gone into creating such a thorough and comprehensive reference, and I have no doubt it will be an important and useful addition to the literature on this subject." (Mark Hunacek, The Mathematical Gazette, 90:19, 2006)

"The focus of this book is the study of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. … the book is largely self-contained. … the authors are extremely knowledgeable in their subjects and the reader can profit from the wealth of material contained in this book. Therefore this book is an ideal reference source and research guide for graduate students and mathematicians working in this area." (Benjamin Cahen, Zentralblatt MATH, Vol. 1068, 2005)

"The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. … The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included." (L’Enseignement Mathematique, Vol. 51 (3-4), 2006)

"This introduction to Lie algebras and algebraic groups aims to provide a full background to the subject. … The book has an encyclopedic character, offering much else besides the actual subject." (Mathematika, Vol. 52, 2005)

"The stated goal of the authors is to provide a ‘foundation for the study of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero’ in a self-contained work that will be useful to ‘both graduate students and mathematicians working in this area’. … the book contains a wealth of detail and takes the reader from the basic classical concepts to the modern borders of this still-active area. Complete proofs are given and the authors present their material clearly and concisely throughout." (Duncan Melville, MathDL, March, 2006)

"This book offers ... complete presentation of the theory of the topics in its title over an algebraically closed field of characteristic zero. Assuming only an undergraduate background in abstract algebra, it covers in detail all the prerequisites that one needs for the theory of Lie algebras and algebraic groups together with the foundations of that theory. ... The book is well written and easy to follow ... ." (William M. McGovern, SIAM Reviews, Vol. 48 (1), 2006)

"The theory of algebraic groups and Lie algebras is a deeply advanced and developed area of modern mathematics. … The text is clearly written and the material is well organized and considered, so the present book may be strongly recommended both to a beginner looking for a self-contained introduction to the theory of algebraic groups and Lie algebras, and to a specialist who wants to have a systematic presentation of the theory." (Ivan V. Arzhantsev, Mathematical Reviews, Issue, 2006 c)