Algebras of Functions on Quantum Groups: Part I PDF Download

Author: Leonid I. Korogodski
Publisher: American Mathematical Soc.
ISBN: 0821803360
Category : Function algebras
Languages : en
Pages : 162

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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: Anatoli Klimyk
Publisher: Springer Science & Business Media
ISBN: 3642608965
Category : Science
Languages : en
Pages : 568

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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: Leonid I. Korogodski
Publisher:
ISBN: 9780821803363
Category : Function algebras
Languages : en
Pages : 149

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Book Description

Author: George Lusztig
Publisher: Springer Science & Business Media
ISBN: 0817647171
Category : Mathematics
Languages : en
Pages : 352

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Book Description
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Author: L. C. Biedenharn
Publisher: World Scientific
ISBN: 9810223315
Category : Science
Languages : en
Pages : 305

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Book Description
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.

Author: Masud Chaichian
Publisher: World Scientific
ISBN: 9789810226237
Category : Science
Languages : en
Pages : 362

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Book Description
In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.

Author: Thomas Timmermann
Publisher: European Mathematical Society
ISBN: 9783037190432
Category : Mathematics
Languages : en
Pages : 436

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Book Description
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: Florin Felix Nichita
Publisher: MDPI
ISBN: 3038973246
Category : Mathematics
Languages : en
Pages : 239

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Book Description
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms

Author: Petr P. Kulish
Publisher: Springer
ISBN: 9783540553052
Category : Mathematics
Languages : en
Pages : 0

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Book Description
The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.

Author: Naihuan Jing
Publisher: World Scientific
ISBN: 9814485500
Category : Science
Languages : en
Pages : 172

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Book Description
Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics. This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields. Contents:Uno's Conjecture on Representation Types of Hecke Algebras (S Ariki)Quiver Varieties, Afine Lie Algebras, Algebras of BPS States, and Semicanonical Basis (I Frenkel et al.)Divided Differences of Type D and the Grassmannian of Complex Structures (H Duan & P Pragacz)Tableaux Statistics For Two Part Macdonald Polynomials (L Lapointe & J Morse)A Crystal to Rigged Configuration Bijection for Nonexceptional Affine Algebras (M Okado et al.)Littlewood's Formulas for Characters of Orthogonal and Symplectic Groups (A Lascoux)A q-Analog of Schur's Q-Functions (G Tudose & M Zabrocki) Readership: Researchers and graduate students in algebraic combinatorics, representation theory and quantum groups. Keywords:Algebras;Representation Theory;Polynomid;Varities;Q-Functions