装饰根森林上的自由余圈无穷小单位Hopf代数

doi:10.3969/j.issn.1006­-8074.2022.02.006

数学理论与应用

装饰根森林上的自由余圈无穷小单位Hopf代数

张毅*, 曹靖涵, 吴笑醒

南京信息工程大学数学与统计学院，南京, 210044

出版日期:2022-06-28

Free Cocycle Infinitesimal Unitary Hopf Algebra on Decorated Rooted Forests

Zhang Yi*, Cao Jinghan , Wu Xiaoxing

School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044, China

Online:2022-06-28
Contact: Zhang Yi(1990-), Lecturer, PhD, Research interests: Rota-Baxter algebra and Hopf algebra; E-mail: zhangy2016@nuist.edu.cn
Supported by:
This work is supported by National Natural Science Foundation of China (No. 12101316, 11801275)

摘要/Abstract

摘要：

本文在根森林的无穷小双代数上赋予一个对径点, 使之进一步成为一个无穷小单位Hopf代数; 然后, 从算子代数的框架中考虑此无穷小单位Hopf 代数, 提出余圈无穷小单位Hopf 代数的概念, 其中涉及到一个无穷小Hochschild 1-余圈条件; 最后, 证明装饰平面根森林的底空间带上一族嫁接运算是一个集合上的自由余圈无穷小单位Hopf代数.

关键词: 根森林, 无穷小Hopf代数, 算子代数, 预李代数

Abstract: In this paper, we equip an infinitesimal bialgebra on rooted forests with an antipode such that it is further an infinitesimal unitary Hopf algebra. Viewing this infinitesimal unitary Hopf algebra in the framework of operated algebras, we then propose the concept of cocycle infinitesimal unitary Hopf algebra, which involves an infinitesimal Hochschild 1-cocycle condition. Finally, we prove that the space of decorated planar rooted forests together with a family of grafting operations is the free cocycle infinitesimal unitary Hopf algebra on a set.

Key words: Rooted forest, Infinitesimal Hopf algebra, Operated algebra, Pre-Lie algebra

张毅, 曹靖涵, 吴笑醒. 装饰根森林上的自由余圈无穷小单位Hopf代数[J]. 数学理论与应用, doi: 10.3969/j.issn.1006-8074.2022.02.006.

Zhang Yi, Cao Jinghan, Wu Xiaoxing. Free Cocycle Infinitesimal Unitary Hopf Algebra on Decorated Rooted Forests[J]. Mathematical Theory and Applications, doi: 10.3969/j.issn.1006-8074.2022.02.006.

装饰根森林上的自由余圈无穷小单位Hopf代数

Free Cocycle Infinitesimal Unitary Hopf Algebra on Decorated Rooted Forests

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