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Reconstruction of graded groupoids from graded Steinberg algebras

Pere Ara EMAIL logo , Joan Bosa , Roozbeh Hazrat and Aidan Sims
From the journal Forum Mathematicum


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

Communicated by Manfred Droste

Award Identifier / Grant number: DP150101598

Funding statement: 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.


We are very grateful to the referee, whose helpful comments have significantly improved the exposition of the paper, and have also suggested interesting lines of further enquiry.


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Received: 2016-3-15
Revised: 2016-8-30
Published Online: 2016-10-11
Published in Print: 2017-9-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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