|Table of Contents|

[1] FU Ruolei, WANG Shuanhong,. Weak Hopf bornological algebras [J]. Journal of Southeast University (English Edition), 2026, 42 (3): 406-410. [doi:10.3969/j.issn.1003-7985.2026.03.013]
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Weak Hopf bornological algebras()
弱有界型Hopf代数

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
42
Issue:
2026 3
Page:
406-410
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2026-09-06

Info

Title:
Weak Hopf bornological algebras
弱有界型Hopf代数
Author(s):
FU Ruolei, WANG Shuanhong
School of Mathematics, Southeast University, Nanjing 210096, China
付若磊, 王栓宏
东南大学数学学院, 南京 210096
Keywords:
(weak) Hopf bornological algebra;  weak Hopf algebra;  Lie groupoid;  locally convex space
(弱)有界型Hopf代数;  弱Hopf代数;  李群胚;  局部凸空间
PACS:
O153
DOI:
10.3969/j.issn.1003-7985.2026.03.013
Abstract:
We introduce the notion of a weak Hopf bornological algebra, which simultaneously generalizes the classical frameworks of weak Hopf algebras and Hopf bornological algebras. This extension aims to unify algebraic structures with topological boundedness structures, thereby providing a natural setting for the treatment of Hopf-type objects arising in locally convex spaces and groupoid algebras. First, we present the definition and basic properties of weakly bounded Hopf algebras and prove some basic results analogous to those in weak Hopf algebras, such as the uniqueness of the antipode and its anti-homomorphic properties with respect to the multiplication and comultiplication. Finally, we mainly study the weak Hopf bornological algebra structure on finite Lie groupoids. Several basic examples are explicitly constructed, and their comultiplications, antipodes, and counits are computed in detail. These results indicate that the weak boundedness condition can be naturally derived from the composition law of finite Lie groupoids. Overall, this theoretical framework offers a new perspective for studying Hopf-type algebras and provides a novel approach for investigating symmetry and duality in bounded and analytic contexts.
本文引入了弱有界型Hopf代数的概念,该对象同时推广了弱Hopf代数与有界型Hopf代数的经典框架。此推广旨在将代数结构与拓扑有界型结构统一起来,以更自然地处理出现在局部凸空间与群胚代数中的Hopf型结构。本文首先给出了弱有界型Hopf代数的定义与基本性质,证明了若干与一般弱Hopf代数类似的重要结果,如反对极的唯一性及其对乘法、余乘法的反同态性。最后,研究了有限李群胚上的弱有界型Hopf代数结构,构造了若干基本例子,并计算了它们的余乘、对极与余单位。结果表明,弱有界条件可由有限李群胚的复合律自然导出。该理论框架为Hopf型代数的研究提供了新的视角,也为有界型与解析情形下的对称性与对偶性研究开辟了新途径。

References:

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Memo

Memo:
Received: 2025-08-09; Revised: 2025-10-09.
Biographies: FU Ruolei (1999—), male, Ph.D.candidate; WANG Shuanhong (corresponding author), male, doctor, professor, 101010505@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China (No.12271089, 12471033).
Citation: FU Ruolei, WANG Shuanhong. Weak Hopf bornological algebras[J]. Journal of Southeast University (English Edition), 2026, 42(3): 406-410. DOI: 10. 3969/j. issn. 1003-7985. 2026. 03. 013.
Last Update: 2026-09-20