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" Quasi-Hopf algebras : "
Daniel Bulacu (Universitatea din Bucureti, Romania), Stefaan Caenepeel (Vrije Universiteit, Amsterdam), Florin Panaite (Institute of Mathematics of the Romanian Academy), Freddy van Oystaeyen (Universiteit Antwerpen, Belgium).
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BL
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839653
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| Main Entry
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Bulacu, Daniel,1973-
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| Title & Author
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Quasi-Hopf algebras : : a categorical approach /\ Daniel Bulacu (Universitatea din Bucureti, Romania), Stefaan Caenepeel (Vrije Universiteit, Amsterdam), Florin Panaite (Institute of Mathematics of the Romanian Academy), Freddy van Oystaeyen (Universiteit Antwerpen, Belgium).
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| Publication Statement
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Cambridge ;New York, NY :: Cambridge University Press,, [2019]
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| Series Statement
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Encyclopedia of mathematics and its applications ;; 171
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1 online resource
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| ISBN
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1108582788
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: 1108632653
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: 9781108582780
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: 9781108632652
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1108427014
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9781108427012
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Includes bibliographical references and index.
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| Contents
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Cover; Half-title; Series information; Title page; Copyright information; Dedication; Contents; Preface; 1 Monoidal and Braided Categories; 1.1 Monoidal Categories; 1.2 Examples of Monoidal Categories; 1.2.1 The Category of Sets; 1.2.2 The Category of Vector Spaces; 1.2.3 The Category of Bimodules; 1.2.4 The Category of G-graded Vector Spaces; 1.2.5 The Category of Endo-functors; 1.2.6 A Strict Category Associated to a Monoidal Category; 1.3 Monoidal Functors; 1.4 Mac Lane's Strictification Theorem for Monoidal Categories; 1.5 (Pre- )Braided Monoidal Categories; 1.6 Rigid Monoidal Categories
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1.7 The Left and Right Dual Functors1.8 Braided Rigid Monoidal Categories; 1.9 Notes; 2 Algebras and Coalgebras in Monoidal Categories; 2.1 Algebras in Monoidal Categories; 2.2 Coalgebras in Monoidal Categories; 2.3 The Dual Coalgebra/Algebra of an Algebra/Coalgebra; 2.4 Categories of Representations; 2.5 Categories of Corepresentations; 2.6 Braided Bialgebras; 2.7 Braided Hopf Algebras; 2.8 Notes; 3 Quasi-bialgebras and Quasi-Hopf Algebras; 3.1 Quasi-bialgebras; 3.2 Quasi-Hopf Algebras; 3.3 Examples of Quasi-bialgebras and Quasi-Hopf Algebras
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3.4 The Rigid Monoidal Structure of HMfd and MHfd3.5 The Reconstruction Theorem for Quasi-Hopf Algebras; 3.6 Sovereign Quasi-Hopf Algebras; 3.7 Dual Quasi-Hopf Algebras; 3.8 Further Examples of (Dual) Quasi-Hopf Algebras; 3.9 Notes; 4 Module (Co)Algebras and (Bi)Comodule Algebras; 4.1 Module Algebras over Quasi-bialgebras; 4.2 Module Coalgebras over Quasi-bialgebras; 4.3 Comodule Algebras over Quasi-bialgebras; 4.4 Bicomodule Algebras and Two-sided Coactions; 4.5 Notes; 5 Crossed Products; 5.1 Smash Products; 5.2 Quasi-smash Products and Generalized Smash Products
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5.3 Endomorphism H-module Algebras5.4 Two-sided Smash and Crossed Products; 5.5 H*-Hopf Bimodules; 5.6 Diagonal Crossed Products; 5.7 L-R-smash Products; 5.8 A Duality Theorem for Quasi-Hopf Algebras; 5.9 Notes; 6 Quasi-Hopf Bimodule Categories; 6.1 Quasi-Hopf Bimodules; 6.2 The Dual of a Quasi-Hopf Bimodule; 6.3 Structure Theorems for Quasi-Hopf Bimodules; 6.4 The Categories [sub(H)]M[sub(H)sup(H)] and [sub(H)]M; 6.5 A Structure Theorem for Comodule Algebras; 6.6 Coalgebras in [sub(H)]M[sub(H)sup(H)]; 6.7 Notes; 7 Finite-Dimensional Quasi-Hopf Algebras; 7.1 Frobenius Algebras
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| Abstract
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This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
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Hopf algebras.
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Tensor algebra.
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Tensor products.
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Hopf algebras.
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MATHEMATICS-- Algebra-- Intermediate.
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Tensor algebra.
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Tensor products.
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| Dewey Classification
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512/.55
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| LC Classification
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QA613.8.B85 2019eb
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| Added Entry
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Caenepeel, Stefaan,1956-
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Oystaeyen, F. Van,1947-
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Panaite, Florin,1970-
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