Mathematical Sciences: RUI: Structural Problems of Limit Subalgebras of AF C* -Algebras

小行星9500566哈德逊 非自伴算子代数理论，特别是近似有限C*-代数的极限子代数理论，近年来得到了迅速的发展。拟议的研究涉及的结构的三角AF代数及其格的理想，激进的结构和分类的各种类型的理想在三角AF代数，因子分解问题在算子代数，几何单位球的三角AF代数，代数拓扑考虑的背景下，算子代数。 运算符可以被看作是复数的有限或无限矩阵。通过这种方式，一个算子的集合通常可以被赋予一个代数结构，并被称为算子代数。在处理其元素可以实现为无限矩阵的算子代数的情况下，重要的是要理解代数是如何构造的，或者可以近似为有限矩阵。近似有限算子代数是有限维子代数的极限。 这些研究将有助于理解这些自然算子代数的结构。 ***

9500566 Hudson The theory of nonselfadjoint operator algebras, and in particular, the theory of limit subalgebras of approximately finite C*-algebras, has experienced rapid development in recent years. The proposed research concerns the structure of triangular AF algebras and their lattices of ideals, the radical structure and classification of various types of ideals in triangular AF algebras, factorization questions in operator algebras, the geometry of the unit ball of triangular AF algebras, and algebraic topology considerations within the context of operator algebras. Operators can be viewed as finite or infinite matrices of complex numbers. In this way a collection of operators can often be given an algebraic structure and referred to as an operator algebra. In the case where one is dealing with operator algebras whose elements can be realized as infinite matrices, it is important to understand how the algebra is constructed or can be approximated out of finite matrices. An approximately finite operator algebra is a limit of finite dimensional subalgebras. This research will contribute to understanding the structure of these natural operator algebras. ***