Mathematical Sciences: Index Reduction Formulas for Central Simple Alge>ras.

数学科学：中心简单代数的指数约简公式>ras。

• 批准号: 9307596
• 负责人: Adrian Wadsworth
• 金额: $ 6万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307596&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Index; Reduction; Formulas

This work is concerned with the study of index reduction formulas for central simple algebras on passage to the function field of a projective variety. The type of variety under consideration is a twisted form of G/P where G is a split reductive algebraic group and P is a parabolic subgroup of G. The index reduction formula will follow from a knowledge of the Grothendieck group of the variety of interest, which has been computed in general only when G is connected. The principal investigator will investigate the Grothendieck group of the twisted forms of G/P when G is not connected, where it is clear from examples that some new phenomena not seen in the connected case will arise. The principal investigator will also study central simple algebras with involution, and the associated generalized even Clifford algebras. 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.

本文主要研究指数约简问题 中心单代数关于函数的公式 射影簇的域。 品种类型 考虑的是G/P的扭曲形式，其中G是分裂 约化代数群，P是G的抛物子群。 索引缩减公式将根据以下知识得出： Grothendieck集团的各种利益，这一直是 一般只在G连通时计算。 校长 调查人员将调查格罗滕迪克集团的 当G不连接时，G/P的扭曲形式，很明显 从例子中，一些新的现象没有看到在连接 案件将出现。首席研究员还将研究 具有对合的中心单代数， 广义偶Clifford代数 这项研究是在环理论的一般领域。 的环 是既有加法又有加法的代数对象 乘法定义。虽然加法运算 满足交换律，乘法运算是 不需要这样做。 一个环的例子， 乘法不是交换的是nxn的集合 整数上的矩阵。 非交换环的研究 已经成为代数的一个重要组成部分，因为它的增长 对数学和物理学的其他分支具有重要意义。