具有理想性质的AH代数的分类及其应用

自上世纪80年代，加拿大数学家G. A. Elliott利用K理论的序群对AF代数进行成功分类以来，Elliott不变量便成了研究C*代数同构分类的热点。2007年，G.A. Elliott、G. Gong、L. Li完成了对于单的、距离空间的维数不增长的AH代数的彻底分类。此后，去掉单的、实秩零的条件利用Elliott不变量对AH代数进行分类成为一个重要的研究课题。而具有理想性质的AH代数则成为此课题中重要的研究对象，一个AH代数被称为具有理想性质，是指如果这个AH代数的每个双边理想都是其理想中的投影生成的。本课题的主要目的是希望通过丰富Elliott不变量，从而对具有理想性质的AH代数进行分类，并以期以期在其它数学分支中找到应用。

Since Canadian mathematician G.A. Elliott gave a successful classification of AF algebras with the ordered K-group in 1980's, Elliott invariants became one of the research hotspots of classification of C*-algebras. In 2007, the classification theorem for the simple AH algebras with no dimension growth was obtained G.A. Elliott、G. Gong、L. Li . After that, to give a classification theorem for the AH algebras without conditions of simple or real rank zero properties is an important object. And the reseraches on AH algebra with the ideal property becomes more important. An AH algebra with the ideal property means that each of two sides ideal is generated by it's projections. This subject is mainly concerned about the classification of AH algebra with the ideal property by increasing the numbers of Elliott invariants and application of the other branches.