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 -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