标题： 关于图C*-代数和勒维特定向图代数的内马克问题 显示英文标题

标题： Naimark's Problem for graph C*-algebras and Leavitt path algebras

摘要： 我们描述了如何利用图中的边界路径来构造与该图对应的 C*-代数和Leavitt路径代数的不可约表示。 基于这一构造，我们得到了两组结果：首先，我们证明了Naimark问题对于图C*-代数有肯定的答案；我们还证明了Naimark问题的代数类比对于Leavitt路径代数也有肯定的答案，并给出了图满足Naimark问题假设条件的充要条件。 其次，我们刻画了图C*-代数具有可数（即有限或可数无穷）谱的条件，并证明在这种情况下，不可约表示的酉等价类与图的边界路径的移位尾等价类之间存在一一对应关系。 显示英文摘要

摘要： We describe how boundary paths in a graph can be used to construct irreducible representations of the associated graph C*-algebra and the associated Leavitt path algebra. We use this construction to establish two sets of results: First, we prove that Naimark's Problem has an affirmative answer for graph C*-algebras, we prove that the algebraic analogue of Naimark's Problem has an affirmative answer for Leavitt path algebras, and we give necessary and sufficient conditions on the graphs for the hypotheses of Naimark's Problem to be satisfied. Second, we characterize when a graph C*-algebra has a countable (i.e., finite or countably infinite) spectrum, and prove that in this case the unitary equivalence classes of irreducible representations are in one-to-one correspondence with the shift-tail equivalence classes of the boundary paths of the graph.