Amplified graph C*-algebras II: Reconstruction

@article{Eilers2020AmplifiedGC,
  title={Amplified graph C*-algebras II: Reconstruction},
  author={S{\o}ren Eilers and Efren Ruiz and Aidan Sims},
  journal={Proceedings of the American Mathematical Society, Series B},
  year={2020}
}
<p>Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a countable directed graph that is amplified in the sense that whenever there is an edge from <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="v… 

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References

SHOWING 1-10 OF 29 REFERENCES

Graph algebras and orbit equivalence

We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every

Refined moves for structure-preserving isomorphism of graph C*-algebras

We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose

Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras

Let A,B be square irreducible matrices with entries in {0,1}. We will show that if the one-sided topological Markov shifts (X_A,\sigma_A) and (X_B,\sigma_B) are continuously orbit equivalent, then

Leavitt path algebras of separated graphs

Abstract The construction of the Leavitt path algebra associated to a directed graph E is extended to incorporate a family C consisting of partitions of the sets of edges emanating from the vertices

Amplified graph C*-algebras

We provide a complete invariant for graph C*-algebras which are amplified in the sense that whenever there is an edge between two vertices, there are infinitely many. The invariant used is the

$C^*$-algebras of directed graphs and group actions

Given a free action of a group $G$ on a directed graph $E$ we show that the crossed product of $C^* (E)$, the universal $C^*$-algebra of $E$, by the induced action is strongly Morita equivalent to

Stability of C^*-algebras associated to graphs

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each

The C^*-algebras of infinite graphs

::: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ::: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

We prove that ample groupoids with sigma-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani

Classification of irreversible and reversible Pimsner operator algebras

Abstract Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint