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A Tour of Representation Theory

Martin Lorenz Temple University, Philadelphia, PA
Available Formats:
Hardcover ISBN: 978-1-4704-3680-3
Product Code: GSM/193
List Price: $94.00 MAA Member Price:$84.60
AMS Member Price: $75.20 Electronic ISBN: 978-1-4704-4905-6 Product Code: GSM/193.E List Price:$94.00
MAA Member Price: $84.60 AMS Member Price:$75.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $141.00 MAA Member Price:$126.90
AMS Member Price: $112.80 Click above image for expanded view A Tour of Representation Theory Martin Lorenz Temple University, Philadelphia, PA Available Formats:  Hardcover ISBN: 978-1-4704-3680-3 Product Code: GSM/193  List Price:$94.00 MAA Member Price: $84.60 AMS Member Price:$75.20
 Electronic ISBN: 978-1-4704-4905-6 Product Code: GSM/193.E
 List Price: $94.00 MAA Member Price:$84.60 AMS Member Price: $75.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$141.00 MAA Member Price: $126.90 AMS Member Price:$112.80
• Book Details

Volume: 1932018; 654 pp
MSC: 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 self-study.

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
• Finite-dimensional Hopf algebras
• Appendices
• The language of categories and functors
• Background from linear algebra
• Some commutative algebra
• The Diamond Lemma
• The symmetric ring of quotients

• 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 self-study.

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 well-prepared 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 graduate-level representation theory.

Mark Hunacek, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1932018; 654 pp
MSC: 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 self-study.

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
• Finite-dimensional 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 self-study.

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 well-prepared 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 graduate-level representation theory.

Mark Hunacek, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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