Algebraic Geometry of Partially Commutative Groups

部分交换群的代数几何

• 批准号: EP/D065275/1
• 负责人: Andrew Duncan
• 金额: $ 2.09万
• 依托单位: Newcastle University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD065275%2F1
• 关键词: Algebraic; Geometry; Partially; Commutative; Groups

Solving equations and describing their solutions has always been a central part of mathematics. Here we have equations which are framed in terms of groups and for which we seek solutions in groups. We know how to describe solutions to equations over Abelian groups and to equations in one variiable in free groups. This project considers a class of groups that contains free and Abelian groups but yet is simple to describe and which is amenable to analysis. Our eventual aim is to understand solutions to equations over these groups, but to make progress we are restricting attention to equations of one variable. We allso intend to make some preliminary investigations into areas of group theory (related to equations) where there are some difficult problems that we think we may have some techniques to solve.

求解方程和描述其解一直是数学的核心部分。在这里我们有方程，这些方程是以群为单位的，我们在群中求解。我们知道如何描述阿贝尔群上的方程和自由群中的单变量方程的解。这个项目考虑一类包含自由和阿贝尔群的群，但它易于描述和分析。我们的最终目标是了解这些群体方程的解决方案，但为了取得进展，我们将注意力限制在一个变量的方程上。我们也打算对群论（与方程有关）的一些领域进行一些初步的研究，在这些领域中有一些困难的问题，我们认为我们可能有一些技术来解决。

项目成果

Parabolic and quasiparabolic subgroups of free partially commutative groups

自由部分交换群的抛物线和拟抛物线子群

• DOI: 10.1016/j.jalgebra.2007.08.032
• 发表时间: 2007
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Duncan A

Orthogonal Systems in Finite Graphs

有限图中的正交系统

• DOI: 10.48550/arxiv.0707.0087
• 发表时间: 2007
• 作者: Duncan A

Centraliser Dimension of Partially Commutative Groups

部分交换群的中心维数

• DOI: 10.1007/s10711-006-9046-3
• 发表时间: 2006
• 期刊: Geometriae Dedicata
• 影响因子: 0.5
• 作者: Duncan A

Automorphisms of partially commutative groups I: Linear subgroups

部分交换群 I 的自同构：线性子群

• DOI: 10.4171/ggd/103
• 发表时间: 2010
• 期刊: Groups, Geometry, and Dynamics
• 作者: Duncan A