Mathematical Sciences: On the Classification of the Simple, Stably Finite, Separable, Amenable C-Algebras

数学科学：关于简单、稳定有限、可分离、适用的 C 代数的分类

• 批准号: 9622250
• 负责人: Guihua Gong
• 金额: $ 4.84万
• 依托单位: University of Puerto Rico-Rio Piedras
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622250&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Classification; Simple; Stably

DMS-9622250 PI: Gong The ASH algebras (or AH algebras, respectively) are the C*-algebras arising as inductive limits of direct sums of subalgebras (or corner subalgebras, respectively) of matrix algebras over commutative C*-algebras. These algebras play an essential role in the Elliott program for the classification of separable amenable C*-algebras. The investigators propose to construct ASH (or AH) inductive limit decompositions for C*-algebras with certain general properties --- and, in particular, to prove the conjecture that any simple separable amenable C*-algebra of real rank zero and stable rank one is an AH algebra. They also propose to classify arbitrary simple ASH algebras in terms of the K-theory and tracial state space invariants (used, in special cases, by Elliott and others including the investigators). The passage from a finite to an infinite number of degrees of freedom in quantum physics led to the mathematical theory of certain infinite dimensional algebras, called operator algebras. A complete enumeration (or classification) of a special class of operator algebras, called (amenable) von Neumann algebras, was eiven by A. Connes in his Fields Medal winning work of 1975. (The Fields Medal is the equivalent of the Nobel Prize in mathematics.) More recently, V. F. R. Jones has applied the theory of von Neumann algebras to study ordinary knots. This work, which also won a Fields Medal, has shed light on quantum physics, and on the structure of DNA. The investigators propose to work on a complete enumeration (or classification) of another important class of operator algebras, called amenable C*-algebras. The successful classification of such C*-algebras will be essential for us to understand the infinite dimensional world of quantum physics.

DMS-9622250 PI：Gong ASH代数（或AH代数）是C*-代数 产生的 子代数（或角）直和的归纳极限 交换环上矩阵代数的 C*-代数这些代数在艾略特 可分离顺从C*-代数的分类程序。的 研究者们建议构造ASH（或AH）归纳极限 分解的C*-代数具有某些一般性质--和， 特别是，证明了猜想，任何简单的可分服从 真实的秩为零且稳定秩为一的C*-代数是AH代数。他们 我还建议分类任意单ASH代数的条款， K理论和迹状态空间不变量（在特殊情况下， 埃利奥特和其他人，包括调查人员）。 从有限自由度到无限自由度的过渡 在量子物理学中，导致了某种无限的数学理论 维代数，称为算子代数。一个完整的枚举（或 分类）的一类特殊的算子代数，称为（顺从） von Neumann代数是由A.康纳斯在他的 菲尔兹奖得主 1975年的工作。(The菲尔兹奖相当于年的诺贝尔奖。 数学）。最近，V.F. R.琼斯运用了 冯诺依曼代数来研究普通的纽结。 这项工作，这也赢得了 菲尔兹奖，揭示了量子物理学，并对结构， DNA.调查人员建议进行一次全面的调查（或 分类）的另一类重要的算子代数，称为 顺从C*-代数这类C ~*-代数的成功分类 对我们理解宇宙的无限维度世界至关重要 量子物理学