Reconstruction of graded groupoids from graded Steinberg algebras
Rings and Algebras
2020-02-25 v2 Operator Algebras
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 -isomorphism of -algebras for graphs and in which every cycle has an exit.
Keywords
Cite
@article{arxiv.1601.02872,
title = {Reconstruction of graded groupoids from graded Steinberg algebras},
author = {Pere Ara and Joan Bosa and Roozbeh Hazrat and Aidan Sims},
journal= {arXiv preprint arXiv:1601.02872},
year = {2020}
}
Comments
18 pages. Revised version, to appear in Forum Mathematicum