可能行无限图C＊-代数

The C~*-Algebras of Possibly Row-Infinite Directed Graphs

本文研究可能行无限有向图的C*-代数．对于一个可能行无限的有向图E，通过引进集合s(μν)，将行无限点上的算子拓扑强收敛关系代数化表示出来，并由此构造了一个结构丰富的非零*-代数HE，进而利用HE证明了一个由Cuntz-Krieger E-族{se，pv}生成的泛C*-代数C*(E)的存在性，并且证明了HE和C*(E)在图同构意义下不依赖于E的选择，从而是可能行无限有向图的同构不变量．

This paper is about the C~*-algebras of possibly row-infinite directed graphs. For a possibly row-infinite directed graph E, we introduce the set s(μ,ν), by which the strong operator topology on the row-infinite vertices is algebraically represented. Moreover, a *-algebra H_E with rich structure is constructed, by which the existence of the universal C~*-algebra generated by Cuntz-Krieger E-family {s_e, p_ν} is proved. We also proved that the H_E and C~*(E) are the isomorphism invariants of E.