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Let E be a countable directed graph that is amplified in the sense that whenever there is an edge from v to w, there are infinitely many edges from v to w. We show that E can be recovered from C^*(E) together with its canonical gauge-action, and also from L_\mathbb {K}(E) together with its canonical grading. [ABSTRACT FROM AUTHOR]

We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and finitely or countably infinitely many edges, corresponding to unital and separable C*-algebras. [ABSTRACT FROM AUTHOR]

We give a complete description of which unital graph C ⁎ -algebras are semiprojective, and use it to disprove two conjectures by Blackadar. To do so, we perform a detailed analysis of which projections are properly infinite in such C ⁎ -algebras. [ABSTRACT FROM AUTHOR]

There are many classes of nonsimple graph C*-algebras that are classified by the six-term exact sequence in K-theory. In this paper we consider the range of this invariant and determine which cyclic six-term exact sequences can be obtained by various classes of graph C*-algebras. To accomplish this, we establish a general method that allows us to form a graph with a given sixterm exact sequence of K-groups by splicing together smaller graphs whose C*- algebras realize portions of the six-term exact sequence. As rather immediate consequences, we obtain the first permanence results for extensions of graph C*-algebras. We are hopeful that the results and methods presented here will also prove useful in more general cases, such as situations where the C*-algebras under investigation have more than one ideal and where there are currently no relevant classification theories available. [ABSTRACT FROM AUTHOR]

Close ties between approximation properties for relations on C*-algebra elements and lifting results for the universal C*-algebras the relations generate is a very widespread and useful phenomenon in C*-algebra theory. In this paper, we explore how to achieve results of this kind when the approximation properties and the lifting results are true only in special cases determined by K-theoretical contingencies. To interpolate between properties of these two basic types, we must investigate C*-algebras given by softened relations, in particular with emphasis on their K-theory. A surprisingly weak correlation between the K-theory of the C*-algebras given by exact and softened relations leads to delicate problems which must be treated with care. As an example of a set of relations which are prone to an analysis of this kind we study the pairs of unitaries commuting up to rational rotation. [ABSTRACT FROM AUTHOR]