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Author: Anatoli Klimyk Publisher: Springer Science & Business Media ISBN: 3642608965 Category : Science Languages : en Pages : 568
Book Description
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: Anatoli Klimyk Publisher: Springer Science & Business Media ISBN: 3642608965 Category : Science Languages : en Pages : 568
Book Description
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: Naihuan Jing Publisher: American Mathematical Soc. ISBN: 1470436965 Category : Algebra Languages : en Pages : 233
Book Description
This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.
Author: Seok-Jin Kang Publisher: American Mathematical Soc. ISBN: 0821805126 Category : Lie algebras Languages : en Pages : 242
Book Description
Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
Author: Peter Woit Publisher: Springer ISBN: 3319646125 Category : Science Languages : en Pages : 668
Book Description
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Author: A Varchenko Publisher: World Scientific ISBN: 981450162X Category : Mathematics Languages : en Pages : 384
Book Description
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik–Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals. Contents:IntroductionConstruction of Complexes Calculating Homology of the Complement of a ConfigurationConstruction of Homology Complexes for Discriminantal ConfigurationAlgebraic Interpretation of Chain Complexes of a Discriminantal ConfigurationQuasiisomorphism of Two-Sided Hochschild Complexes to Suitable One-Sided Hochschild ComplexesBundle Properties of a Discriminantal ConfigurationR-Matrix for the Two-Sided Hochschild ComplexesMonodromyR-Matrix Operator as the Canonical Element, Quantum DoublesHypergeometric IntegralsKac–Moody Lie Algebras Without Serre's Relations and Their DoublesHypergeometric Integrals of a Discriminantal ConfigurationResonances at InfinityDegenerations of Discriminantal ConfigurationsRemarks on Homology Groups of a Configuration with Coefficients in Local Systems More General than Complex One-Dimensional Readership: Mathematicians, theoretical physicists, and graduate students. keywords:Hypergeometric Function;Hypergeometric Type Function;Hypergeometric Integral;Kac-Moody Algebra;Quantum Group;Representations of a Kac-Moody Algebra;Representations of a Quantum Group;Discriminant Configuration;Monodromy “The book is elegantly structured and sticks closely to the point, and is also fairly down to earth … as well as serving as an excellent specialist monograph, it should also be useful as a first exposure to these topics for anyone who likes to learn a subject through the study of a concrete problem.” Bull. London Math. Soc.
Author: Anatoliĭ Moiseevich Vershik Publisher: CRC Press ISBN: 9782881246784 Category : Mathematics Languages : en Pages : 576
Book Description
Eight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Author: Vlastimil Dlab Publisher: American Mathematical Soc. ISBN: 0821834169 Category : Associative algebras Languages : en Pages : 502
Book Description
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Author: Leonid I. Korogodski Publisher: American Mathematical Soc. ISBN: 0821803360 Category : Function algebras Languages : en Pages : 162
Book Description
The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.
Author: Niky Kamran Publisher: American Mathematical Soc. ISBN: 0821851691 Category : Mathematics Languages : en Pages : 310
Book Description
This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.
Author: Anatoli Klimyk
Author: Anatoli Klimyk
Author: Naihuan Jing
Author: Naihuan Jing
Author: Seok-Jin Kang
Author: Peter Woit
Author: A Varchenko
Author: Anatoliĭ Moiseevich Vershik
Author: Vlastimil Dlab
Author: Leonid I. Korogodski
Author: Niky Kamran