作者：王志华
页数：150
出版社：科学出版社
出版日期：2024
ISBN：9787030781468
电子书格式：pdf/epub/txt
内容简介
本书在Hopf代数表示范畴层面引入一些新的monoidal不变量，这些不变量包括表示范畴的Green环、Casimir数、高阶Frobenius-Schur指标、Grothendieck环、某种类型的多元齐次多项式等。著作主要研究这些不变量在Hopf代数表示理论中所发挥的作用，揭示这些不变量与Hopf代数表示范畴中其它重要研究对象之间的关系，通过具体实例展示这些不变量的具体表现形式等。这些不变量的引入为人们研究Hopf代数表示范畴的结构与分类提供了新的工具，也为人们深入理解与研究monoidal范畴提供了新的视角。本书所展示的一些研究成果对于推动代数表示理论体系的发展与完善，促进Hopf代数、张量范畴等数学分支的交叉与融合具有积极的作用。
作者简介
王志华，男，1980年11月出生，江苏东台人，泰州学院教授。2014年取得比利时Hasselt大学博士学位，2015年取得扬州大学博士学位，2017—2019年进入南京大学博士后流动站从事博士后工作，2019年人选江苏高校“青蓝工程”中青年学术带头人培养对象。工作以来在国内外期刊上发表学术论文四十多篇。
目录
《博士后文库》序言
Preface
Chapter 1 The Green Rings of Hopf Algebras
1.1 Hopf algebras
1.2 Quantum traces ofmorphisms
1.3 Bilinear forms on Green rings
1.4 Some ring—theoretical properties
Chapter 2 The Green Rings of Spherical Hopf Algebras
2.1 A new bilinear form
2.2 Quotients of Green rings
2.3 Group—like algebra and bi—Frobenius algebra structure
Chapter 3 The Stable Green Rings of Hopf Algebras
3.1 Stable Green rings
3.2 Bi—Frobenius algebra structure
3.3 Applications to Radford Hopf algebras
Chapter 4 The Caslmlr Numbers of Green Rings
4.1 The Jacobson semisimplicity of Green rings
4.2 The Green ring of a cyclic group
4.3 The Casimir number of the Green ring of a cyclic group
Chapter 5 The Casimir Numbers of Fusion Categories
5.1 Numerical invariants
5.2 Applications to Verlinde modular categories
5.3 Prime factors of Casimir numbers
5.4 Casimir numbers VS.Frobenius—Schur exponents
Chapter 6 Higher Frobenius.Schur Indicators in Positive Characteristic
6.1 Characterizations of S2=id
6.2 Some properties of the element U
6.3 Higher Frobenius—Schur indicators
6.4 Monoidal invariantS
Chapter 7 The Grothendieck Algebras of Smash Product Hopf Algebras
7.1 Smash product Hopf algebras
7.2 Representations of smash product Hopf algebras
7.3 The Grothendieck algebras of smash product Hopf algebras
Chapter 8 Invariants from the Sweedler Power Maps on Integrals
8.1 The Sweedler power maps on integrals
8.2 Polynomial invariants
8.3 Examples
8.4 Integrals of the dual of twisted Hopf algebras
Bibliography
Index
编后记
Preface
Chapter 1 The Green Rings of Hopf Algebras
1.1 Hopf algebras
1.2 Quantum traces ofmorphisms
1.3 Bilinear forms on Green rings
1.4 Some ring—theoretical properties
Chapter 2 The Green Rings of Spherical Hopf Algebras
2.1 A new bilinear form
2.2 Quotients of Green rings
2.3 Group—like algebra and bi—Frobenius algebra structure
Chapter 3 The Stable Green Rings of Hopf Algebras
3.1 Stable Green rings
3.2 Bi—Frobenius algebra structure
3.3 Applications to Radford Hopf algebras
Chapter 4 The Caslmlr Numbers of Green Rings
4.1 The Jacobson semisimplicity of Green rings
4.2 The Green ring of a cyclic group
4.3 The Casimir number of the Green ring of a cyclic group
Chapter 5 The Casimir Numbers of Fusion Categories
5.1 Numerical invariants
5.2 Applications to Verlinde modular categories
5.3 Prime factors of Casimir numbers
5.4 Casimir numbers VS.Frobenius—Schur exponents
Chapter 6 Higher Frobenius.Schur Indicators in Positive Characteristic
6.1 Characterizations of S2=id
6.2 Some properties of the element U
6.3 Higher Frobenius—Schur indicators
6.4 Monoidal invariantS
Chapter 7 The Grothendieck Algebras of Smash Product Hopf Algebras
7.1 Smash product Hopf algebras
7.2 Representations of smash product Hopf algebras
7.3 The Grothendieck algebras of smash product Hopf algebras
Chapter 8 Invariants from the Sweedler Power Maps on Integrals
8.1 The Sweedler power maps on integrals
8.2 Polynomial invariants
8.3 Examples
8.4 Integrals of the dual of twisted Hopf algebras
Bibliography
Index
编后记
