Mathematical Sciences: Invariants for Abelian Groups and Representations of Posets

本研究的主要目的是研究 一类无挠Abel群的不变量 被称为巴特勒集团不变量将被检查 同时，在有限部分表示的上下文中， 有序集 Coxeter对应与几乎分裂的研究 序列被列入该项目的目的是扩大 潜在可分类组和表示的菜单。 这项研究是在代数的一般领域， 关于无限群的结构理论， 交换乘法结构-阿贝尔群。 这些 群出现在代数、几何和 分析. 本研究涉及不变量的分类 为这些阿贝尔群的选定家庭， 得到一般结构理论。

The primary goal of this research is the study of the invariants for a class of torsion-free Abelian groups of finite rank known as the Butler groups. The invariants are to be examined concurrently in the context of representations of finite partially ordered sets. A study of Coxeter correspondences and almost split sequences is included in the project with the aim of expanding the menu of potentially classifiable groups and representations. The research is in the general area of algebra and is concerned with the structure theory of infinite groups having a commutative multiplicative structure - the Abelian groups. These groups arise in a variety of settings in algebra, geometry, and analysis. This research concerns the classification of invariants for selected families of these Abelian groups in anticipation of obtaining a general structure theory.