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Softcover ISBN:  9780821853351 
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Softcover ISBN:  9780821853351 
Product Code:  MMONO/100.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470416553 
Product Code:  MMONO/100.S.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821853351 
eBook ISBN:  9781470416553 
Product Code:  MMONO/100.S.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 100; 1992; 245 ppMSC: Primary 14; Secondary 20
The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups.
Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
ReadershipGraduate students and research mathematicians interested in invariant theory.

Table of Contents

Chapters

Introduction

Notation and terminology

Chapter 1. The role of reductive groups in invariant theory

Chapter 2. Constructive invariant theory

Chapter 3. The degree of the Poincaré series of the algebra of invariants and a finiteness theorem for representations with free algebra of invariants

Chapter 4. Syzygies in invariant theory

Chapter 5. Representations with free modules of covariants

Chapter 6. A classification of normal affine quasihomogeneous varieties of $SL_2$

Chapter 7. Quasihomogeneous curves, surfaces, and solids


Reviews

The book is a good reference for specialists in invariant theory and stimulating for nonexperts.
Zentralblatt MATH


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The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups.
Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
Graduate students and research mathematicians interested in invariant theory.

Chapters

Introduction

Notation and terminology

Chapter 1. The role of reductive groups in invariant theory

Chapter 2. Constructive invariant theory

Chapter 3. The degree of the Poincaré series of the algebra of invariants and a finiteness theorem for representations with free algebra of invariants

Chapter 4. Syzygies in invariant theory

Chapter 5. Representations with free modules of covariants

Chapter 6. A classification of normal affine quasihomogeneous varieties of $SL_2$

Chapter 7. Quasihomogeneous curves, surfaces, and solids

The book is a good reference for specialists in invariant theory and stimulating for nonexperts.
Zentralblatt MATH