Hardcover ISBN:  9781470436803 
Product Code:  GSM/193 
List Price:  $94.00 
MAA Member Price:  $84.60 
AMS Member Price:  $75.20 
Electronic ISBN:  9781470449056 
Product Code:  GSM/193.E 
List Price:  $94.00 
MAA Member Price:  $84.60 
AMS Member Price:  $75.20 

Book DetailsGraduate Studies in MathematicsVolume: 193; 2018; 654 ppMSC: Primary 16; 17; 20;
Representation theory investigates the different ways in which a given algebraic object—such as a group or a Lie algebra—can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry.
Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory.
The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by selfstudy.ReadershipGraduate students and researchers interested in various aspects of representation theory.

Table of Contents

Algebras

Representations of algebras

Further topics on algebras

Groups

Groups and group algebras

Symmetric groups

Lie algebras

Lie algebras and enveloping algebras

Semisimple Lie algebras

Root systems

Representations of semisimple Lie algebras

Hopf algebras

Coalgebras, bialgebras, and Hopf algebras

Representations and actions

Affine algebraic groups

Finitedimensional Hopf algebras

Appendices

The language of categories and functors

Background from linear algebra

Some commutative algebra

The Diamond Lemma

The symmetric ring of quotients


Additional Material

Reviews

Complemented by more than 350 exercises at various levels of difficulty, this text is a valuable reference for researchers and students in algebra and related fields, and is ideally suitable for learning representation theory by selfstudy.
Dongwen Liu, Mathematical Reviews 
This excellent book is one that I wish had been written when I was a student...Had I the benefit of a book like this one in my early graduate years, I could have saved myself a lot of time...This is a very nicely written book, with student motivation always in mind. The level of difficulty increases as the book proceeds (as is only reasonable) but at no point does the book become too difficult for a wellprepared graduate student reader...I like this book a lot, and consider it to be a very valuable addition to the existing textbook literature on representation theory. It would not surprise me if it becomes the market leader in books on graduatelevel representation theory.
Mark Hunacek, MAA Reviews


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Representation theory investigates the different ways in which a given algebraic object—such as a group or a Lie algebra—can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry.
Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory.
The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by selfstudy.
Graduate students and researchers interested in various aspects of representation theory.

Algebras

Representations of algebras

Further topics on algebras

Groups

Groups and group algebras

Symmetric groups

Lie algebras

Lie algebras and enveloping algebras

Semisimple Lie algebras

Root systems

Representations of semisimple Lie algebras

Hopf algebras

Coalgebras, bialgebras, and Hopf algebras

Representations and actions

Affine algebraic groups

Finitedimensional Hopf algebras

Appendices

The language of categories and functors

Background from linear algebra

Some commutative algebra

The Diamond Lemma

The symmetric ring of quotients

Complemented by more than 350 exercises at various levels of difficulty, this text is a valuable reference for researchers and students in algebra and related fields, and is ideally suitable for learning representation theory by selfstudy.
Dongwen Liu, Mathematical Reviews 
This excellent book is one that I wish had been written when I was a student...Had I the benefit of a book like this one in my early graduate years, I could have saved myself a lot of time...This is a very nicely written book, with student motivation always in mind. The level of difficulty increases as the book proceeds (as is only reasonable) but at no point does the book become too difficult for a wellprepared graduate student reader...I like this book a lot, and consider it to be a very valuable addition to the existing textbook literature on representation theory. It would not surprise me if it becomes the market leader in books on graduatelevel representation theory.
Mark Hunacek, MAA Reviews