Internal Categories And Quantum Groups

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Internal Categories And Quantum Groups

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Author : Marcelo Aguiar
language : en
Publisher:
Release Date : 1997

Internal Categories And Quantum Groups written by Marcelo Aguiar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Tensor Categories

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Author : Pavel Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-05

Tensor Categories written by Pavel Etingof and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Foundations Of Quantum Group Theory

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Author : Shahn Majid
language : en
Publisher: Cambridge University Press
Release Date : 2000

Foundations Of Quantum Group Theory written by Shahn Majid and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Group theory categories.

A graduate level text which systematically lays out the foundations of Quantum Groups.

Quantum Groups

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Author : Ross Street
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-18

Quantum Groups written by Ross Street and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-18 with Mathematics categories.

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.

A Guide To Quantum Groups

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Author : Vyjayanthi Chari
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-27

A Guide To Quantum Groups written by Vyjayanthi Chari and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-27 with Mathematics categories.

Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.

Categories For Quantum Theory

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Author : Chris Heunen
language : en
Publisher:
Release Date : 2019

Categories For Quantum Theory written by Chris Heunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.

Categories for Quantum Theory: An Introduction lays foundations for an approach to quantum theory that uses category theory, a branch of pure mathematics. Prior knowledge of quantum information theory or category theory helps, but is not assumed, and basic linear algebra and group theory suffices.

Homological Algebra Of Semimodules And Semicontramodules

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Author : Leonid Positselski
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02

Homological Algebra Of Semimodules And Semicontramodules written by Leonid Positselski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.

This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.

Affine Lie Algebras And Quantum Groups

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Author : Jürgen Fuchs
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-09

Affine Lie Algebras And Quantum Groups written by Jürgen Fuchs and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-09 with Mathematics categories.

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Introduction To Quantum Groups

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Author : Masud Chaichian
language : en
Publisher: World Scientific
Release Date : 1996

Introduction To Quantum Groups written by Masud Chaichian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.

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.

Logic Language Information And Computation

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Author : Lev D. Beklemishev
language : en
Publisher: Springer
Release Date : 2011-04-28

Logic Language Information And Computation written by Lev D. Beklemishev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-28 with Mathematics categories.

This book constitutes the refereed proceedings of the 18th Workshop on Logic, Language, Information and Communication, WoLLIC 2011, held in Philadelphia, PA, USA, in May 2011. The 21 revised full papers presented were carefully reviewed and selected from 35 submissions. Among the topics covered are various aspects of mathematical logic, computer science logics, philosophical logics, such as complexity theory, model theory, partial order, Hoare logics, hybrid logics, Turing machines, etc.