Softcover ISBN:  9781470441876 
Product Code:  ULECT/69 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470443467 
Product Code:  ULECT/69.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9781470441876 
eBook: ISBN:  9781470443467 
Product Code:  ULECT/69.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 
Softcover ISBN:  9781470441876 
Product Code:  ULECT/69 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470443467 
Product Code:  ULECT/69.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9781470441876 
eBook ISBN:  9781470443467 
Product Code:  ULECT/69.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 69; 2017; 153 ppMSC: Primary 15; 14; 20
This book gives a unified, complete, and selfcontained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of \(m\times m\) matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation.
Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving
(1) the first fundamental theorem that describes a set of generators in the ring of invariants, and
(2) the second fundamental theorem that describes relations between these generators.
The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, selfcontained way in the book.
The print version of this book is only available in black and white. The eBook is in full color.
ReadershipUndergraduate and graduate students and researchers interested in linear algebra, representation theory, and invariant theory.

Table of Contents

Chapters

Introduction and preliminaries

The classical theory

Quasihereditary algebras

The Schur algebra

Matrix functions and invariants

Relations

The Schur algebra of a free algebra


Additional Material

Reviews

The present book is a nice and introductory reference to graduate students or researchers who are working in the field of representation and invariant theory.
Yin Chen, Zentralblatt MATH 
The choices made by the authors permit them to highlight the main results and also to keep the material within the reach of an interested reader. At the same time, the book remains openended with precise pointers to the literature on other approaches and the cases not treated here.
Felipe Zaldivar, MAA Reviews


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This book gives a unified, complete, and selfcontained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of \(m\times m\) matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation.
Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving
(1) the first fundamental theorem that describes a set of generators in the ring of invariants, and
(2) the second fundamental theorem that describes relations between these generators.
The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, selfcontained way in the book.
The print version of this book is only available in black and white. The eBook is in full color.
Undergraduate and graduate students and researchers interested in linear algebra, representation theory, and invariant theory.

Chapters

Introduction and preliminaries

The classical theory

Quasihereditary algebras

The Schur algebra

Matrix functions and invariants

Relations

The Schur algebra of a free algebra

The present book is a nice and introductory reference to graduate students or researchers who are working in the field of representation and invariant theory.
Yin Chen, Zentralblatt MATH 
The choices made by the authors permit them to highlight the main results and also to keep the material within the reach of an interested reader. At the same time, the book remains openended with precise pointers to the literature on other approaches and the cases not treated here.
Felipe Zaldivar, MAA Reviews