罗巴型代数,Hom-结构和Stirling数

批准号:
11961031
项目类别:
地区科学基金项目
资助金额:
41.0 万元
负责人:
郑上华
依托单位:
学科分类:
群与代数的结构
结题年份:
2023
批准年份:
2019
项目状态:
已结题
项目参与者:
郑上华
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中文摘要
罗巴代数来自于积分算子的代数抽象和推广。由于罗巴代数在数学和理论物理中有着广泛的应用,因此它已发展成为一个公认的新兴领域。罗巴型代数作为一类特殊的带算子代数,起源于美国数学家Rota提出的关于代数上线性算子分类的公开问题。近年来,罗巴型代数在代数性质和结构上与罗巴代数相似,因而也得到了广泛的研究。本项目拟开展有关罗巴型代数的三个方面研究。第一方面是将罗巴型算子和修改罗巴算子进行融合,引入广义罗巴型代数概念,并研究其相关代数结构和经典代数上的广义罗巴型算子的分类;第二个方面,将罗巴代数中的Stirling数,多项式系数与划分之间的密切关系拓展到它们与罗巴型代数的联系,进而引入Stirling型数;第三个方面,基于我们对Hom-罗巴代数的研究,我们将借助于组合对象根树或括号字构造Hom-罗巴型代数的自由对象,并利用cocycle条件研究自由Hom-罗巴型代数上的Hom-Hopf代数结构。
英文摘要
A Rota-Baxter algebra is drawn from an algebraic abstraction and generalization of the integration operators. Since Rota-Baxter algebra has a wide range of applications in mathematics and theoretical physics, it has already been developed into an emerging field of research. As a special kind of operated algebras, Rota-Baxter type algebras originated from the study of the problem of classifying all linear operators on an algebra, which was proposed by the American mathematician Rota. Recently, Rota-Baxter type algebras have been extensively investigated because it resembles Rota-Baxter algebras in algebraic properties and structures. This project intends to carry out three aspects of study on Rota-Baxter type algebras. The first aspect is to combine Rota-Baxter operators and modified Rota-Baxter operators and introduce the concept of generalized Rota-Baxter type algebras. We further study the related algebraic structures and the classification of generalized Rota-Baxter type operators in classical algebras. In the second aspect, the close relationship between Stirling numbers, multimonial coefficients and partitions with Rota-Baxter algebras is extended to introduce Stirling type numbers by their connection with Rota-Baxter type algebras. In the third aspect, based on our experience with Hom-Rota-Baxter algebras, the free objects of Hom-Rota-Baxter type algebras are constructed by means of combination objects such as rooted trees or bracketed words, and the Hom-Hopf algebraic structures on free Hom-Rota-Baxter type algebras are investigated by means of cocycle conditions.
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DOI:10.1007/s10801-023-01281-z
发表时间:2022-07
期刊:Journal of Algebraic Combinatorics
影响因子:0.8
作者:Shanghua Zheng;Li Guo
通讯作者:Shanghua Zheng;Li Guo
DOI:10.1142/s0219498824500993
发表时间:2022-07
期刊:Journal of Algebra and Its Applications
影响因子:0.8
作者:Hengyi Luo;Shanghua Zheng
通讯作者:Hengyi Luo;Shanghua Zheng
DOI:https://doi.org/10.1080/00927872.2023.2301518
发表时间:2024
期刊:Communications in Algebra
影响因子:--
作者:Qiu Huizhen;Zheng Shanghua;Dan Yangfan
通讯作者:Dan Yangfan
DOI:--
发表时间:2021
期刊:Southeast Asian Bulletin of Mathematics
影响因子:0.2
作者:Zheng Shanghua;Shum K. P.
通讯作者:Shum K. P.
罗巴算子与自由模上的项重写系统
- 批准号:11601199
- 项目类别:青年科学基金项目
- 资助金额:19.0万元
- 批准年份:2016
- 负责人:郑上华
- 依托单位:
国内基金
海外基金
