Factorized Groups, Yang-Baxter Equation and local Nearrings
因式分解群、Yang-Baxter 方程和局部近环
基本信息
- 批准号:317529529
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2016
- 资助国家:德国
- 起止时间:2015-12-31 至 2017-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Groups which can be written as a product G = AB of two subgroups A and B have been studied by many authors. A particular role in such investigations play triply factorized groups of the form G = AB = AM = BM with subgroups A, B and a normal subgroup M of G such that the intersections between A and M resp. B and M are trivial. It turns out that if M is abelian, then there exists a one-to-one correspondence between these groups and so-called braces. These are generalized radical rings which arise in the study of set-theoretical solutions of the quantum Yang-Baxter equation. In the case, when the subgroup M is non-abelian, triply factorized groups can be constructed using some nearrings, especially so-called local nearrings. This means that many problems concerning the structure of braces and local nearrings can be reduced to some questions about the structure of triply factorized groups and vice versa. We will study different aspects of this connection and, in addition, consider certain structural questions about factorized groups G = AB arising in the case when the two subgroups A and B have abelian subgroups of small index.
许多作者已经研究了可以写成两个子群 A 和 B 的乘积 G = AB 的群。在此类研究中,一个特殊的角色是具有 G = AB = AM = BM 形式的三因式分解群,其中包含子群 A、B 和 G 的正规子群 M,使得 A 和 M 之间的交集分别为: B 和 M 是微不足道的。事实证明,如果 M 是交换矩阵,那么这些群和所谓的大括号之间就存在一一对应关系。这些是在研究量子杨-巴克斯特方程的集合论解时出现的广义基环。在这种情况下,当子群 M 是非阿贝尔时,可以使用一些近环,特别是所谓的局部近环来构造三重因式分解群。这意味着有关大括号和局部近环结构的许多问题可以简化为有关三重分解群结构的一些问题,反之亦然。我们将研究这种联系的不同方面,此外,考虑当两个子群 A 和 B 具有小索引的阿贝尔子群时出现的因式分解群 G = AB 的某些结构问题。
项目成果
期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On products of groups with abelian subgroups of small index
关于具有小指数阿贝尔子群的群的乘积
- DOI:10.1515/jgth-2017-0008
- 发表时间:
- 期刊:
- 影响因子:0.5
- 作者:Amberg
- 通讯作者:Amberg
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Professor Dr. Bernhard Amberg其他文献
Professor Dr. Bernhard Amberg的其他文献
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