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• 2010009598 abstract "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. Table of Contents: Quantum disc; Basic quantum theory of bounded symmetric domains; Conclusion; Bibliography; Index. About the book: 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.".
• 2010009598 alternative "Kvantovye ogranichennye simmetricheskie oblasti. English".
• 2010009598 contributor B11748080.
• 2010009598 created "c2010.".
• 2010009598 date "2010".
• 2010009598 date "c2010.".
• 2010009598 dateCopyrighted "c2010.".
• 2010009598 description "Ch. 1. Quantum Disc -- 1.1. A caution to pedants -- 1.2. Topology -- 1.3. Symmetry -- 1.4. An invariant integral -- 1.5. Differential calculi -- 1.6. Integral representations -- 1.7. On kernels of intertwining integral operators -- Ch. 2. Basic quantum theory of bounded symmetric domains -- 2.1. Summary on quantum universal enveloping algebras -- 2.2. Summary on algebras of functions on compact quantum groups -- 2.3. Quantum vector spaces and Harish-Chandra modules -- 2.4. Spaces of functions in quantum bounded symmetric domains -- 2.5. The canonical embedding -- 2.6. Covariant differential calculi and invariant differential operators -- Ch. 3. Conclusion -- 3.1. Boundaries and spherical principal series -- 3.2. The analytic continuation of holomorphic discrete series and the Penrose transform.".
• 2010009598 description "Includes bibliographical references and index.".
• 2010009598 description "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. Table of Contents: Quantum disc; Basic quantum theory of bounded symmetric domains; Conclusion; Bibliography; Index. About the book: 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.".
• 2010009598 extent "xi, 256 p. :".
• 2010009598 identifier "0821849093 (alk. paper)".
• 2010009598 identifier "9780821849095 (alk. paper)".
• 2010009598 isPartOf "Translations of mathematical monographs ; v. 238".
• 2010009598 isPartOf "Translations of mathematical monographs ; v. 238.".
• 2010009598 issued "2010".
• 2010009598 issued "c2010.".
• 2010009598 language "Translated from the Russian.".
• 2010009598 language "eng rus".
• 2010009598 language "eng".
• 2010009598 publisher "Providence, R.I. : American Mathematical Society,".
• 2010009598 subject "512/.55 22".
• 2010009598 subject "Noncommutative algebras.".
• 2010009598 subject "QC20.7.F84 V3513 2010".
• 2010009598 subject "Quantum groups.".
• 2010009598 subject "Representations of quantum groups.".
• 2010009598 subject "Symmetric domains.".
• 2010009598 tableOfContents "Ch. 1. Quantum Disc -- 1.1. A caution to pedants -- 1.2. Topology -- 1.3. Symmetry -- 1.4. An invariant integral -- 1.5. Differential calculi -- 1.6. Integral representations -- 1.7. On kernels of intertwining integral operators -- Ch. 2. Basic quantum theory of bounded symmetric domains -- 2.1. Summary on quantum universal enveloping algebras -- 2.2. Summary on algebras of functions on compact quantum groups -- 2.3. Quantum vector spaces and Harish-Chandra modules -- 2.4. Spaces of functions in quantum bounded symmetric domains -- 2.5. The canonical embedding -- 2.6. Covariant differential calculi and invariant differential operators -- Ch. 3. Conclusion -- 3.1. Boundaries and spherical principal series -- 3.2. The analytic continuation of holomorphic discrete series and the Penrose transform.".
• 2010009598 title "Kvantovye ogranichennye simmetricheskie oblasti. English".
• 2010009598 title "Quantum bounded symmetric domains / Leonid L. Vaksman ; translated by Olga Bershtein and Sergey D. Sinel'shchikov.".
• 2010009598 type "text".