Diagonal-preserving graded isomorphisms of Steinberg 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 $C^{\ast }$-algebras.

arXiv comment23 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

References in corpus (5)

• Homology and topological full groups of etale groupoids on totally disconnected spaces
• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
• The Path Space of a Directed Graph
• Graph algebras and orbit equivalence
• $C^{\ast }$-algebras associated to Boolean dynamical systems

Cited by in corpus (6)

• Reconstruction of groupoids and C*-rigidity of dynamical systems
• Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids
• Topological Full Groups of Ample Groupoids with Applications to Graph Algebras
• The dynamics of partial inverse semigroup actions
• Reconstruction of twisted Steinberg algebras
• Tensor products of Steinberg algebras