Mathematical Sciences: Homological Methods in the Deformation Theory of Operator Algebras

DMS-9623314 PI：Nagy堪萨斯州立大学 Nagy将研究C*-代数中的刚性现象 形变量子化为了解决这些问题， 纳吉计划使用和发展同源技术足以 C*-代数的分类。一个动机 这项研究是最近全世界的兴趣， 一种新的量子群理论，它将几个分支联系在一起 它是数学的一部分，与数学物理密切相关。 这个项目的另一个动机和灵感是开发 在与非交换几何有关的C*-代数的K-理论中。 数学领域的这个项目有其基础理论的代数算子的希尔伯特空间。 算子代数的研究始于20世纪30年代， 约翰·冯·诺依曼为了提供一个数学框架 量子力学。算子代数由于其广泛的应用，是目前数学中最具活力的领域之一。例如，算子代数的显著相互作用 与20世纪80年代沃恩·琼斯发现的纽结理论相结合， 在DNA分子研究中的有趣应用由于其 在非对易几何学，量子概率论， 在共形量子场论中，算子代数 在物理学中变得越来越重要。

DMS-9623314 PI: Nagy Kansas State University Nagy will investigate rigidity phenomena in C*-algebraic deformation quantization. In order to address such problems, Nagy plans to use and develop homological techniques adequate for the classification of certain classes of C*-algebras. One motivation of this research is the recent worldwide interest in the promising new theory of quantum groups which links together several branches of mathematics and is closely related to mathematical physics. Another motivation and inspiration for this project is the development in the K-theory of C*-algebras in connection with non-commutative geometry. The area of mathematics for this project has its basis in the theory of algebras of operators on Hilbert spaces. The study of operator algebras was initiated in the 1930's by John von Neumann in order to provide a mathematical framework for quantum mechanics. Due to a broad range of applications, operator algebras are presently one of the most dynamic fields in mathematics. For example, the remarkable interactions of operator algebras with knot theory, discovered by Vaughan Jones in the 1980's, lead to interesting applications to the study of the DNA molecules. Due to their fundamental role in non-commutative geometry, in quantum probability theory, and in conformal quantum field theory, operator algebras have become increasingly important in physics.