RT Conference Proceedings T1 Reconstruction of graded groupoids from graded Steinberg algebras A1 Ara, Pere K1 Grupos, Teoría de K1 Grupoides AB We show how to reconstruct a graded ample Hausdorff groupoid with topologically principalneutrally-graded component from the ring structure of its graded Steinberg algebra overany commutative integral domain with 1, together with the embedding of the canonicalabelian subring of functions supported on the unit space. We deduce thatdiagonal-preserving ring isomorphism of Leavitt path algebras implies $C^*$-isomorphismof $C^*$-algebras for graphs $E$ and $F$ in which every cycle has an exit.This is a joint work with Joan Bosa, Roozbeh Hazrat and Aidan Sims. YR 2016 FD 2016-05-19 LK http://hdl.handle.net/10630/11432 UL http://hdl.handle.net/10630/11432 LA eng NO Universidad de Málaga. Campus de Excelencia internacional Andalucía Tech DS RIUMA. Repositorio Institucional de la Universidad de Málaga RD 21 ene 2026