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
Funding source: Australian Research Council
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.
Acknowledgements
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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