Mathematical Sciences: Homology and Representations Theory of Finite Dimensional Algebras and Classical Orders

数学科学：有限维代数和经典阶的同调和表示论

• 批准号: 9204182
• 负责人: Birge Huisgen-Zimmermann
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204182&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homology; Representations; Theory

This research is concerned with the homological aspects of finite dimensional algebras. The principal investigator will examine several dimensions which measure the homological complexity of an algebra in order to obtain precise structural descriptions of higher syzygies, and to describe and exploit repetitive homological behavior. There will be a heavy emphasis on crossconnections to related areas. In particular, the principal investigator will seek replacements for the Tarsy conjecture on the global dimension of classical orders over discrete valuation domains. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.

本文研究有限维代数的同调性质。主要研究者将研究几个维度，这些维度测量代数的同调复杂性，以获得更高合点的精确结构描述，并描述和利用重复的同调行为。将非常重视与相关领域的交叉连接。特别是，首席研究员将寻求替代的Tarsy猜想的全球规模的经典秩序在离散估值域。这项研究是在环理论的一般领域。环是一个代数对象，它同时定义了加法和乘法。虽然加法运算满足交换律，但乘法运算不需要这样做。乘法不是交换的环的一个例子是整数上的nxn矩阵的集合。非交换环的研究已经成为代数学的一个重要组成部分，因为它对数学和物理学的其他分支越来越重要。