Mathematical Sciences: Representation Theory of Artin Algebras

数学科学：Artin代数表示论

• 批准号: 9009590
• 负责人: Gordana Todorov
• 金额: $ 1.63万
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9009590&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Artin

This research is concerned with the representation theory of artin algebras. The principal investigator will study idempotent ideals and other generalizations of quasihereditary algebras and their usefulness in the reduction of problems to algebras with fewer simple modules. She will also study contravariantly finite subcategories of finitely generated modules over artin algebras with regard to the finitestic global dimension conjecture and existence of almost split sequences. This research is in the general area of ring theory. A ring is an algebraic structure having both an addition and a multiplication defined on it. These objects arise naturally and are important in many areas of mathematics and physics.

本研究涉及artin代数的表示论。首席研究员将研究幂等理想和准遗传代数的其他推广，以及它们在将问题简化为具有较少简单模块的代数方面的有用性。她还将研究 artin 代数上有限生成模的逆变有限子类，涉及有限全局维度猜想和几乎分裂序列的存在性。 这项研究属于环理论的一般领域。环是一种代数结构，其上定义有加法和乘法。这些物体自然产生，在数学和物理学的许多领域都很重要。