ebooks, audiobooks, and more for reads
Download Compact Matrix Quantum Groups And Their Combinatorics full books in PDF, epub, and Kindle. Read online Compact Matrix Quantum Groups And Their Combinatorics ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author: Amaury Freslon
Publisher: Cambridge University Press
Published: 2023-07-27
Total Pages: 302
ISBN-13: 1009345680
DOWNLOAD EBOOKDownload or read book Compact Matrix Quantum Groups and Their Combinatorics written by Amaury Freslon and published by Cambridge University Press. This book was released on 2023-07-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Anatoli Klimyk
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 568
ISBN-13: 3642608965
DOWNLOAD EBOOKThis book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Author: Sergey Neshveyev
Publisher: SMF
Published: 2013
Total Pages: 0
ISBN-13: 9782856297773
DOWNLOAD EBOOKThe book provides an introduction to the theory of compact quantum groups, emphasizing the role of the categorical point of view in constructing and analyzing concrete examples. The general theory is developed in the first two chapters and is illustrated with a detailed analysis of free orthogonal quantum groups and the Drinfeld-Jimbo $q$-deformations of compact semisimple Lie groups. The next two chapters are more specialized and concentrate on the Drinfeld-Kohno theorem, presented from the operator algebraic point of view. This book should be accessible to students with a basic knowledge of operator algebras and semisimple Lie groups.
Download or read book Compact Quantum Groups and Their Representation Categories written by Sergey Neshveyev and published by SMF. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to the theory of compact quantum groups, emphasizing the role of the categorical point of view in constructing and analyzing concrete examples. The general theory is developed in the first two chapters and is illustrated with a detailed analysis of free orthogonal quantum groups and the Drinfeld-Jimbo $q$-deformations of compact semisimple Lie groups. The next two chapters are more specialized and concentrate on the Drinfeld-Kohno theorem, presented from the operator algebraic point of view. This book should be accessible to students with a basic knowledge of operator algebras and semisimple Lie groups.
Author: Tom Hendrik Koornwinder
Publisher:
Published: 1994
Total Pages: 33
ISBN-13:
DOWNLOAD EBOOKAbstract: "A tutorial introduction is given to general Hopf algebras and to general compact quantum groups. In the definition and further treatment of compact quantum groups C*-algebras are avoided. Contact with Woronowicz's compact matrix quantum groups is made at a later stage."
Download or read book General Compact Quantum Groups written by Tom Hendrik Koornwinder and published by . This book was released on 1994 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A tutorial introduction is given to general Hopf algebras and to general compact quantum groups. In the definition and further treatment of compact quantum groups C*-algebras are avoided. Contact with Woronowicz's compact matrix quantum groups is made at a later stage."
Author: Thomas Timmermann
Publisher: European Mathematical Society
Published: 2008
Total Pages: 436
ISBN-13: 9783037190432
DOWNLOAD EBOOKThis book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.
Download or read book An Invitation to Quantum Groups and Duality written by Thomas Timmermann and published by European Mathematical Society. This book was released on 2008 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.
Author: Vladimir K. Dobrev
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2017-07-10
Total Pages: 406
ISBN-13: 3110427702
DOWNLOAD EBOOKWith applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies
Download or read book Quantum Groups written by Vladimir K. Dobrev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-07-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies
Download or read book A Remark on Compact Matrix Quantum Groups written by S. L. Woronowicz and published by . This book was released on 1990 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Susumu Ariki
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 169
ISBN-13: 0821832328
DOWNLOAD EBOOKThis book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and toapply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A {r-1 {(1) $ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be thecombinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, andrelated fields.
Download or read book Representations of Quantum Algebras and Combinatorics of Young Tableaux written by Susumu Ariki and published by American Mathematical Soc.. This book was released on 2002 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and toapply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A {r-1 {(1) $ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be thecombinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, andrelated fields.
Download or read book General Constructions of Compact Quantum Groups written by Shuzhou Wang and published by . This book was released on 1993 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Teo Banica
Publisher: Springer Nature
Published: 2023-01-01
Total Pages: 428
ISBN-13: 3031238176
DOWNLOAD EBOOKThis book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group. Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more. The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter–Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models. Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.
Download or read book Introduction to Quantum Groups written by Teo Banica and published by Springer Nature. This book was released on 2023-01-01 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group. Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more. The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter–Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models. Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.
