Mathematical Sciences: Noncommutative Rings

数学科学：非交换环

• 批准号: 9400643
• 负责人: Martin Lorenz
• 金额: $ 7.5万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-05-01 至 1997-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400643&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Noncommutative; Rings

Lorenz This award supports research in ring theory, focusing on the representation theory of rings of invariants under finite group actions. Particular attention will be given to the structure of the Grothendieck groups, G_0(R) and K_0(R), for certain specific types of invariant rings R. The main objective for G_0(R) is to give a description in terms of Brauer characters of the acting group. Especially important in connection with K_0(R) are the Hattori-Stallings trace and, more general, the Chern characters in cyclic homology. While part of this project will concern the classical commutative setting, in particular linear actions on polynomial rings and multiplicative actions on Laurent polynomial rings, the investigation of certain classes of noncommutative invariants will also be pursued. This topic promises a rich interplay between the areas of commutative and noncommutative ring theory, representation theory of finite groups, homological algebra, and algebraic K-theory. A ring is an algebraic object having both an addition and a multiplication defined on it. These structures arise naturally in many different settings and are of interest in mathematics, computer science, engineering and physics. ***

Lorenz 该奖项支持环理论的研究，重点是有限群作用下的不变量环的表示理论。 特别注意Grothendieck群G_0（R）和K_0（R）的结构， 对于某些特定类型的不变环R。G_0（R）的主要目的是给出作用群的Brauer特征标的刻画。 与K_0（R）有关的特别重要的是Hattori-Stallings迹，更一般的是循环同调中的Chern特征标。 虽然这个项目的一部分将关注经典的交换设置，特别是多项式环上的线性动作和劳伦多项式环上的乘法动作，某些类的非交换不变量的调查也将继续进行。 这一主题承诺交换和非交换环理论，有限群的表示理论，同调代数和代数K-理论领域之间的丰富的相互作用。 环是一个代数对象，它同时定义了加法和乘法。这些结构在许多不同的环境中自然出现，并且在数学，计算机科学，工程和物理学中很有意义。***