Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

Authors

Toke Meier Carlsen, NTNU, Trondheim, Norway, University of the Faroe IslandsFollow
Efren Ruiz, University of Hawaii
Aidan Sims, University of WollongongFollow

RIS ID

112159

Publication Details

Carlsen, T. Meier., Ruiz, E. & Sims, A. (2017). Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras. Proceedings of the American Mathematical Society, 145 (4), 1581-1592.

Abstract

We prove that ample groupoids with σ-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(E₂) and L_Z(E_2-) are not stably *-isomorphic.

Grant Number

ARC/DP150101598