RIS ID
112159
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 LZ(E2) and LZ(E2-) are not stably *-isomorphic.
Grant Number
ARC/DP150101598
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.