Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
By Toke Meier Carlsen, Efren Ruiz, Aidan Sims. 2016
55 citations recorded by the source corpus.
We prove that ample groupoids with sigma-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani equivalence. We use this result to show that diagonal-preserving stable isomorphisms of graph C*-algebras or Leavitt path algebras give rise to isomorphisms of the groupoids of the associated stabilised graphs. We deduce that the Leavitt path algebras $L_Z(E_2)$ and $L_Z(E_{2-})$ are not stably *-isomorphic.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ec6e048ddce3b8df73cc1b3975f0dce890841f4a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
- Aidan Sims
- Efren Ruiz
- Toke Meier Carlsen
- M. Tomforde
- L. O. Clark
- Iain Raeburn
- Ben Steinberg
- Cain Edie-Michell
In Mathematical Physics
Citations in the corpus
- Reconstruction of groupoids and C*-rigidity of dynamical systems (2017, methodology): “For equivalence of (1) and (3)– (5), we just summarise the modifications needed to the arguments of [13].”