부산대학교 도서관

Let E be a finite directed graph with no sources or sinks and write XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 for the graph correspondence. We study the XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0-algebra XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 where XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 is the XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0-algebra generated by weighted shifts on the Fock correspondence XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 given by a weight sequence XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 of operators XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 and XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 is the algebra of compact operators on the Fock correspondence. If XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 for every k, XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 is the Cuntz–Krieger algebra associated with the graph E. We show that XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 can be realized as a Cuntz–Pimsner algebra and use a result of Schweizer to find conditions for the algebra XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 to be simple. We also analyse the gauge-invariant ideals of XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 using a result of Katsura and conditions that generalize the conditions of subsets of XEC∗C∗(E,Z):=T(XE,Z)/KT(XE,Z)C∗F(XE){Zk}Zk∈L(XEk)KZk=IC∗(E,Z)C∗(E,Z)C∗(E,Z)C∗(E,Z)E0 (the vertices of E) to be hereditary or saturated. As an example, we discuss in some details the case where E is a cycle.