Hopf Algebras, Tensor Categories and Related Topics.

Cover
Title page
Contents
Preface
List of speakers and titles of talks
BiHom Hopf algebras viewed as Hopf monoids
Introduction
1. Some combinatorial background
2. Cosemigroups in ⁺-monoidal categories
3. Semigroups in ₊-monoidal categories
4. Bisemigroups in ⁺ ₊-duoidal categories
5. Comonoids in ⁺ ⁰-monoidal categories
6. Monoids in ₀ ₊-monoidal categories
7. Bimonoids in ⁺₀ ⁰₊-duoidal categories
References
Survey on Hopf algebras of GK-dimension 1 and 2
1. Introduction
2. Hopf algebras of GK-dimension 1
3. Hopf algebras of GK-dimension 2
4. Further comments, projects and open questions
Acknowledgments
References
On braided double-biproduct Hopf algebras
Introduction
1. Preliminaries
2. Some braided isomorphisms
3. Double-biproduct Hopf algebras
4. 2-cocycle deformations on double-biproduct Hopf algebras
5. Some examples
Acknowledgments
References
Module Eilenberg-Watts calculus
1. Introduction
2. More about the Eilenberg-Watts calculus
3. Balanced functors and twistings
4. Eilenberg-Watts calculus for module functors
5. Eilenberg-Watts calculus for balanced functors
6. Transporting (co)monads along Eilenberg-Watts
References
Coherent unit actions on braided operads and Hopf algebras
1. Introduction
2. Braided algebraic operads
3. Coherent unit actions and braided -Hopf algebras
4. Criteria for braided binary quadratic regular operads with coherent unit actions
Acknowledgments
References
A novel quantum affine algebra of type ₁⁽¹⁾ and its PBW basis
1. Introduction
2. Admissible quantum affine algebras _{ }(̂ ₂) of type ₁⁽¹⁾
3. New quantum affine algebra _{ }(̂ ₂) of type ₁⁽¹⁾ and its quantum Weyl group
4. Definition of imaginary and real root vectors.

5. A Poincaré-Birkhoff-Witt basis of _{ }(̂ ₂)
Acknowledgments
References
Finite quasi-quantum groups over abelian groups
1. Introduction
2. Normalized cocycles on finite abelian groups and braided Gr-categories
3. Finite quasi-quantum groups of diagonal type: A brief summary
4. Finite quasi-quantum groups of nondiagonal type: A first attempt
5. Some further problems
References
On biproducts and extensions
Introduction
1. Preliminaries
2. The biproduct in the first case
3. Representations
4. Hopf subalgebras of dimension 16
5. Hopf subalgebras of dimension 2
6. Hopf subalgebras of dimensions 4 and 8
7. The biproduct in the second case
References
On the notion of exact sequence: From Hopf algebras to tensor categories
1. Introduction
2. Preliminaries on Hopf algebras and tensor categories
3. Exact sequences of Hopf algebras
4. Exact sequences of tensor categories
5. Exact sequences of finite tensor categories with respect to a module category
6. Examples and open questions
References
Algebraic supergroups and their representations
1. Introduction
2. Algebraic supergroups
3. Representations of algebraic supergroups
4. Quasireductive supergroups admitting maximal parabolic super-subgroups
Acknowledgments
References
Hopf algebraic methods in finite tensor categories: Characters and integrals
1. Introduction
2. Representation theory and Yetter-Drinfeld modules
3. Preliminaries: Finite abelian categories
4. Induction to the Drinfeld center
5. Categorical class functions
6. Integral theory and its applications
7. Applications to fusion categories
Acknowledgments
References
Indecomposability of weak Hopf algebras
1. Introduction
2. Definitions and basic properties related with weak bialgebras.

3. The direct sum construction of weak bialgebras and Hopf algebras
4. The direct sum construction of weak Hopf algebras and quantum doubles
5. Categorical interpretation of the direct sum construction and its generalizations
Acknowledgments
References
Quasi-Hopf algebras of Cartan type and small quasi-quantum groups
1. Introduction
2. Preliminaries
3. Finite-dimensional Quasi-Hopf algebras
4. Genuine Quasi-Hopf algebras of Cartan type
5. Small quasi-quantum groups
References
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