English

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 CC^*-isomorphism of CC^*-algebras for graphs EE and FF 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