Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some m...Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C＊ （E） X（aw） G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T展开更多
基金Supported by National Natural Science Foundation of China （Grant Nos. 10771161, 11071188）
文摘Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E＊ to F, and let （C＊（E）, G,a^w） be the C＊-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C＊ （E） X（aw） G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T
