Title 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)

Published Cambridge ; New York, NY : Cambridge University Press, [2019]

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Description 1 online resource Series Encyclopedia of mathematics and its applications ; 171 Encyclopedia of mathematics and its applications ; 171. Contents 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 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 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 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 Summary This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art Bibliography Includes bibliographical references and index Notes Print version record Subject Hopf algebras. Tensor products. Tensor algebra. MATHEMATICS -- Algebra -- Intermediate. Álgebra tensorial Productos tensoriales Hopf algebras Tensor algebra Tensor products Form Electronic book Author Caenepeel, Stefaan, 1956- author. Panaite, Florin, 1970- author. Oystaeyen, F. Van, 1947- author. ISBN 9781108632652 1108632653 9781108582780 1108582788

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