格原子图C*-代数的性质及相关问题的研究

图C*-代数是算子代数的一个重要课题，也是目前研究的热点。格原子图C*-代数是申请者提出的新概念，它不仅包括图C*-代数、Exel-Laca代数、超图C*-代数，也包括其它类型的C*-代数。本项目将利用图论、格论和图C*-代数的研究技巧，重点研究以下内容：（1）格原子图C*-代数的性质；（2）格原子图C*-代数的度规不变理想和商代数；（3） 格原子图C*-代数与半广群C*-代数的同构关系。本项目的研究将极大地丰富图C*-代数相关理论，具有重要的学术价值。

The theory of graph C*-algebras is very important in operator algebras, and it is also one of the hottest topics in current researches. Lattice atomic graph C*-algebras which put forward by the applicant contain graph C*-algebras, Exel-Laca algebras, ultragraph C*-algebras and other C*-algebras.This project will use the research techniques of graph theory, lattice theory and graph C*-algebras to focuse on the following contents: (1) the properties of the lattice atomic graph C*-algebras; (2) the gauge invariant ideals and quotients of the lattice atomic graph C*-algebras; (3) the isomorphic relation between the lattice atomic graph C*-algebras and the semigroupoid C*-algebras. The research of this project will greatly enrich the theory of graph C*-algebras and has important academic value.