Translated by Olga Bershtein and Sergey D. Sinel'shchikov
Hardcover ISBN:  9780821849095 
Product Code:  MMONO/238 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470416249 
Product Code:  MMONO/238.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821849095 
eBook: ISBN:  9781470416249 
Product Code:  MMONO/238.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Translated by Olga Bershtein and Sergey D. Sinel'shchikov
Hardcover ISBN:  9780821849095 
Product Code:  MMONO/238 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470416249 
Product Code:  MMONO/238.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821849095 
eBook ISBN:  9781470416249 
Product Code:  MMONO/238.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: 238; 2010; 256 ppMSC: Primary 17; 20; 81; Secondary 22; 33; 43; 46
This book provides exposition of the basic theory of quantum bounded symmetric domains. The area became active in the late 1990s at a junction of noncommutative complex analysis and extensively developing theory of quantum groups. It is well known that the classical bounded symmetric domains involve a large number of nice constructions and results of the theory of \(C^*\)algebras, theory of functions and functional analysis, representation theory of real reductive Lie groups, harmonic analysis, and special functions. In a surprising advance of the theory of quantum bounded symmetric domains, it turned out that many classical problems admit elegant quantum analogs. Some of those are expounded in the book. Anyone with an interest in the subject will welcome this unique treatment of quantum groups.
The book is written by a leading expert in a very clear, careful, and stimulating way. I strongly recommend it to graduate students and research mathematicians interested in noncommutative geometry, quantum groups, \(C^*\)algebras, or operator theory.
—Vladimir Drinfeld, University of Chicago
ReadershipGraduate students and research mathematicians interested in representation theory and noncommutative geometry.

Table of Contents

Chapters

Chapter 1. Quantum disc

Chapter 2. Basic quantum theory of bounded symmetric domains

Chapter 3. Conclusion


Additional Material

Reviews

Because of its wide range, detailed expositions and pleasant writing style, the book is an inspiring read for the interested reader.
Mathematical Reviews


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This book provides exposition of the basic theory of quantum bounded symmetric domains. The area became active in the late 1990s at a junction of noncommutative complex analysis and extensively developing theory of quantum groups. It is well known that the classical bounded symmetric domains involve a large number of nice constructions and results of the theory of \(C^*\)algebras, theory of functions and functional analysis, representation theory of real reductive Lie groups, harmonic analysis, and special functions. In a surprising advance of the theory of quantum bounded symmetric domains, it turned out that many classical problems admit elegant quantum analogs. Some of those are expounded in the book. Anyone with an interest in the subject will welcome this unique treatment of quantum groups.
The book is written by a leading expert in a very clear, careful, and stimulating way. I strongly recommend it to graduate students and research mathematicians interested in noncommutative geometry, quantum groups, \(C^*\)algebras, or operator theory.
—Vladimir Drinfeld, University of Chicago
Graduate students and research mathematicians interested in representation theory and noncommutative geometry.

Chapters

Chapter 1. Quantum disc

Chapter 2. Basic quantum theory of bounded symmetric domains

Chapter 3. Conclusion

Because of its wide range, detailed expositions and pleasant writing style, the book is an inspiring read for the interested reader.
Mathematical Reviews