Hopf Algebras, Tensor Categories and Related Topics.

Format:

Book

Author/Creator:

Andruskiewitsch, Nicolás.

Contributor:

Liu, Gongxiang.

Montgomery, Susan.

Series:

Contemporary Mathematics

Contemporary Mathematics ; v.771

Language:

English

Subjects (All):

Hopf algebras.

Tensor algebra.

Geometry, Algebraic.

Physical Description:

1 online resource (372 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

Articles in this volume are based on talks given at the International Workshop on Hopf Algebras and Tensor Categories, held from September 9-13, 2019, at Nanjing University, Nanjing, China.The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras.Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.

Contents:

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

On braided double-biproduct Hopf algebras

1. Preliminaries

2. Some braided isomorphisms

3. Double-biproduct Hopf algebras

4. 2-cocycle deformations on double-biproduct Hopf algebras

5. Some examples

Module Eilenberg-Watts calculus

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

Coherent unit actions on braided operads and Hopf algebras

2. Braided algebraic operads

3. Coherent unit actions and braided -Hopf algebras

4. Criteria for braided binary quadratic regular operads with coherent unit actions

A novel quantum affine algebra of type ₁⁽¹⁾ and its PBW basis

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)

Finite quasi-quantum groups over abelian groups

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

On biproducts and extensions

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

On the notion of exact sequence: From Hopf algebras to tensor categories

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

Algebraic supergroups and their representations

2. Algebraic supergroups

3. Representations of algebraic supergroups

4. Quasireductive supergroups admitting maximal parabolic super-subgroups

Hopf algebraic methods in finite tensor categories: Characters and integrals

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

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

Quasi-Hopf algebras of Cartan type and small quasi-quantum groups

2. Preliminaries

3. Finite-dimensional Quasi-Hopf algebras

4. Genuine Quasi-Hopf algebras of Cartan type

5. Small quasi-quantum groups

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

ISBN:

9781470464271

1470464276

OCLC:

1259591656