Mathematical Sciences: K-Theory of Crossed Products of C*-Algebras by Locally Compact Groups

数学科学：局部紧群 C* 代数的叉积的 K 理论

• 批准号: 9401592
• 负责人: Kevin McClanahan
• 金额: $ 3.4万
• 依托单位: University of Mississippi
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-15 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401592&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Crossed; Products

9401592 McClanahan The investigator has previously shown that Pimsner's most general exact sequence of K-groups is valid in the case of twisted crossed products relative to a circle 2-valued cocycle. One component of the proposed project involves extending this result to the case of unitary multiplier-valued cocycles. A possible application of this result would be the computation of the K-groups of certain group C*-algebras in terms of the K- groups of the group C*-algebras of a normal subgroup and of an action of the corresponding quotient group. The investigator plans to investigate extending Pimsner's exact sequence for groups acting on trees to the partial crossed product setting. This will enable the computation of the K-groups of many other amalgamated products of C*-algebras. This project involves computation of invariants of operator algebras. An operator is an infinite dimensional generalization of matrices. Given the natural algebraic structure a collection of operators can frequently be considered as an algebra. A C*-algebra is an algebra of operators with additional topological structure that is closed under the adjoint operation. A basic problem is to classify operator algebras up to isomorphism. This is frequently handled by determining simple invariants associated with operator algebras. One such invariant is the K-group of a C*-algebra. This project will provide explicit computations of K-groups of product C*-algebras. ***

小行星9401592 研究者先前已经证明，皮姆斯纳的最一般的确切序列的K-群是有效的情况下扭曲的交叉产品相对于一个圆2值上圈。 所提出的项目的一个组成部分，涉及扩展这一结果的情况下，酉乘数值上循环。这个结果的一个可能的应用是用正规子群的群C *-代数的K-群和相应商群的作用来计算某些群C*-代数的K-群。研究人员计划调查扩展Pimsner的确切序列的组作用于树木的部分交叉产品设置。 这将使得计算许多其他C*-代数的合并积的K-群成为可能。 这个项目涉及算子代数的不变量的计算。算子是矩阵的无限维推广。给定自然的代数结构，一个算子的集合经常可以被认为是一个代数。一个C*-代数是一个具有附加拓扑结构的算子代数，它在伴随运算下是封闭的。 一个基本的问题是把算子代数分类到同构。这通常通过确定与算子代数相关的简单不变量来处理。一个这样的不变量是C*-代数的K-群。这个项目将提供乘积C*-代数的K-群的显式计算。 ***