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

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。本文主要研究了三角形AF代数及其理想格的结构、三角形AF代数中各种理想的根结构和分类、算子代数中的因式分解问题、三角形AF代数的单位球几何以及算子代数背景下的代数拓扑考虑。运算符可以看作是有限或无限的复数矩阵。用这种方法，通常可以给算子的集合一个代数结构，并称为算子代数。在处理其元素可以实现为无限矩阵的算子代数的情况下，理解如何构造代数或如何从有限矩阵中近似代数是很重要的。近似有限算子代数是有限维子代数的极限。这项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. ***