Projective modules over function algebras

函数代数上的射影模

• 批准号: 2599012
• 金额: --
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2599012
• 关键词: Projective; modules; over; function; algebras

One of the most basic algebras in function theory is the disc algebra $A(D)$ of complex functions that are continuous on the closed unit disc and holomorphic on the open unit disc. Carlson et al [CCFW] gave examples of Hilbert modules over the disc algebra that are nonzero and projective. Answering a well-known question of Halmos, Pisier [P] constructed a Hilbert module over $A(D)$ that is generated by an operator $T$ that is not similar to a contractive operator. One of the main aims of the project is to produce criteria for Hilbert modules over the disc algebra to be projective. In an apparently separate line of development, Cuntz and Quillen [CQ] introduced the class of quasi- free algebras. An algebra $A$ is quasi-free if the space of noncommutative differential forms is a projective $A$-bimodule. A fundamental example is the algebra of coordinate functions on an algebraic curve. The proposed PhD project will investigate projective modules over function algebras and the connection with and the results of Cuntz and Quillen. The work of Cuntz and Quillen has not yet been absorbed into the literature of operator space theory or fully realized in multivariable operator theory.

函数论中最基本的代数之一是复变函数的圆盘代数A（D），它在闭单位圆盘上是连续的，在开单位圆盘上是全纯的。Carlson等人[CCFW]给出了圆盘代数上的希尔伯特模的例子，这些模是非零的和投射的。为了解决Halmos的一个著名问题，Pisier [P]构造了A（D）上的一个Hilbert模，它是由一个不类似于压缩算子的算子T生成的。该项目的主要目的之一是产生希尔伯特模在圆盘代数上是投射的标准。Cuntz和Quillen [CQ]在一个明显独立的发展路线中引入了拟自由代数类.一个代数$A$是拟自由的，如果非交换微分形式空间是投射$A$-双模。一个基本的例子是代数曲线上的坐标函数的代数。拟议的博士项目将调查投射模函数代数和连接和结果的Cuntz和Quillen。Cuntz和Quillen的工作还没有被吸收到文献的算子空间理论或充分实现在多变量算子理论。