Hopf Algebras and Tensor Categories.

Intro -- Preface -- Conference program -- Unified products and split extensions of Hopf algebras -- Introduction -- 1. Preliminaries -- 2. Unifying products versus split extensions of Hopf algebras -- References -- Hopf monoids in the category of species -- Introduction -- 1. Preliminaries on compositions and partitions -- 2. Species and Hopf monoids -- 3. The Hadamard product -- 4. Set species and set-theoretic Hopf monoids -- 5. Connected Hopf monoids -- 6. The free monoid -- 7. The free commutative monoid -- 8. The free Lie monoid -- 9. Examples of Hopf monoids -- 10. Higher associativity and compatibility -- 11. The bimonoids of set (de)compositions -- 12. Series and functional calculus -- 13. The characteristic operations (Hopf powers) -- 14. Classical idempotents -- 15. The Poincaré-Birkhoff-Witt and Cartier-Milnor-Moore theorems -- 16. The dimension sequence of a connected Hopf monoid -- References -- Classifying Hopf algebras of a given dimension -- 1. Introduction -- 2. Preliminaries -- 3. Hopf algebras of dimension -- 4. Hopf algebras of dimension 8 -- 5. Open cases -- References -- On the double crossed product of weak Hopf algebras -- Introduction -- 1. Double crossed product of weak bialgebras -- 2. The antipode -- 3. Examples -- Appendix A. Diagrams -- References -- The doubles of a braided Hopf algebra -- Introduction -- 1. Preliminaries on categories -- 2. Hopf algebras in braided categories -- 3. Hopf monads -- 4. The central double of a Hopf algebra -- 5. Cross products and cross quotients of Hopf monads -- References -- Induced Conjugacy Classes and Induced _{ }( )-Modules -- 1. Introduction -- 2. Notation -- References -- Recovering information from character tables of Hopf algebras: normality, dimensions and quotients -- introduction -- Preliminaries -- 1. Retrieving information from the character table -- Acknowledgments.

References -- Hom-quasi-bialgebras -- 1. Introduction -- 2. Overview of Hom-associative algebras, Hom-coalgebras and Hom-bialgebras -- 3. Hom-quasi-bialgebras (HQ-bialgebras) -- 4. Gauge Transformation and Drinfeld's Twist Construction for HQ-bialgebras -- 5. Twisted quantum double, an example -- References -- On twisted conjugacy classes of type D in sporadic simple groups -- 1. Introduction -- 2. Preliminaries -- 3. Proof of Theorem 1.1 -- 4. Appendix: the sporadic simple groups -- References -- Partial and unified crossed products are weak crossed products -- Introduction -- 1. The general theory of weak crossed products -- 2. Partial crossed products are weak crossed products -- 3. Unified products are weak crossed products -- References -- The Green rings of the generalized Taft Hopf algebras -- 1. Introduction -- 2. Representation theory of the generalized Taft algebra _{ , } -- 3. Generators and relations for the Green ring ( _{ , }) -- 4. Roots of the generalized Fibonacci polynomials -- 5. Nilpotent elements in ( _{ , }) and representation theory of ( _{ , }) -- 6. Comparing the Green ring and the projective class ring of _{ , } -- Acknowledgments -- References -- Morita equivalence methods in classification of fusion categories -- 1. Introduction -- 2. Definitions and basic notions -- 3. Module categories and categorical Morita equivalence -- 4. Braided fusion categories -- 5. Characterization of Morita equivalence -- 6. Classification results for fusion categories of integral dimensions -- References.

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