English

Diagonal-preserving graded isomorphisms of Steinberg algebras

Rings and Algebras 2018-10-08 v3 Operator Algebras

Abstract

We study Steinberg algebras constructed from ample Hausdorff groupoids over commutative integral domains with identity. We reconstruct (graded) groupoids from (graded) Steinberg algebras and use this to characterise when there is a diagonal-preserving (graded) isomorphism between two (graded) Steinberg algebras. We apply this characterisation to groupoids of directed graphs in order to study diagonal-preserving (graded) isomorphisms of Leavitt path algebras and graph CC^*-algebras.

Keywords

Cite

@article{arxiv.1611.09749,
  title  = {Diagonal-preserving graded isomorphisms of Steinberg algebras},
  author = {Toke Meier Carlsen and James Rout},
  journal= {arXiv preprint arXiv:1611.09749},
  year   = {2018}
}

Comments

23 pages. We have revised our exposition to highlight that we only need to know the ring structure of a Steinberg algebra and its diagonal subalgebra in order to recover the underlying groupoid. This is the version that will be published