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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 29, Issue 5

## Volume 1 (1989)

Pere Ara
• Corresponding author
• Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
• Email
• Other articles by this author:
/ Joan Bosa
• School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW Glasgow,United Kingdom
• Email
• Other articles by this author:
/ Roozbeh Hazrat
/ Aidan Sims
Published Online: 2016-10-11 | DOI: https://doi.org/10.1515/forum-2016-0072

## Abstract

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the embedding of the canonical abelian subring of functions supported on the unit space. We deduce that diagonal-preserving ring isomorphism of Leavitt path algebras implies ${C}^{*}$-isomorphism of ${C}^{*}$-algebras for graphs E and F in which every cycle has an exit.

MSC 2010: 22A22; 20M18; 16S36

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P. Ara, M. Brustenga and G. Cortiñas, K-theory of Leavitt path algebras, Münster J. Math. 2 (2009), 5–34. Google Scholar

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Revised: 2016-08-30

Published Online: 2016-10-11

Published in Print: 2017-09-01

Funding Source: Australian Research Council

Award identifier / Grant number: DP150101598

The first and second-named authors were partially supported by the grants DGI MICIIN MTM2011-28992-C02-01 and MINECO MTM2014-53644-P. The second author is supported by the Beatriu de Pinós fellowship (2014 BP-A 00123). This research was supported by the Australian Research Council grant DP150101598.

Citation Information: Forum Mathematicum, Volume 29, Issue 5, Pages 1023–1037, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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© 2017 Walter de Gruyter GmbH, Berlin/Boston.

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