# 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}
}
• Published 2 July 2020
• Computer Science
• Proceedings of the American Mathematical Society, Series B
<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…
4 Citations
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• 2020
Let $\Gamma$ be the infinite cyclic group on a generator $x.$ To avoid confusion when working with $\mathbb Z$-modules which also have an additional $\mathbb Z$-action, we consider the $\mathbb Let Γ be the infinite cyclic group on a generator x. To avoid confusion when working with Z-modules which also have an additional Z-action, we consider the Z-action to be a Γ-action instead. Starting • Lia Vaš • Mathematics Algebras and Representation Theory • 2023 . The Graded Classiﬁcation Conjecture states that the pointed K gr0 -group is a complete invariant of the Leavitt path algebras of ﬁnite graphs when these algebras are considered with their natural • Mathematics Ergodic Theory and Dynamical Systems • 2022 We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include self-covering ## References SHOWING 1-10 OF 29 REFERENCES • Mathematics Ergodic Theory and Dynamical Systems • 2015 We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every • Mathematics • 2019 We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose Let A,B be square irreducible matrices with entries in {0,1}. We will show that if the one-sided topological Markov shifts (X_A,\sigma_A) and (X_B,\sigma_B) are continuously orbit equivalent, then • Mathematics • 2010 Abstract The construction of the Leavitt path algebra associated to a directed graph E is extended to incorporate a family C consisting of partitions of the sets of edges emanating from the vertices • Mathematics • 2011 We provide a complete invariant for graph C*-algebras which are amplified in the sense that whenever there is an edge between two vertices, there are infinitely many. The invariant used is the • Mathematics Ergodic Theory and Dynamical Systems • 1999 Given a free action of a group$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
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
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• 1999
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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
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Compositio Mathematica
• 2020
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