Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
复制标题
群形的等价性和稳定同构，以及图C*-代数和莱维特路径代数的保对角稳定同构
DOI：
10.1090/proc/13321
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Sims
中科院分区：
文献类型：
--
作者：
T. M. Carlsen;Efren Ruiz;A. Sims
我们证明了充足的群胚与σ紧单位空间是等价的当且仅当它们在适当的意义上是稳定同构的，并将其与Matui的角谷等价概念联系起来。我们使用这个结果表明，图C*-代数或Leavitt路代数的对角保持稳定的同构产生的同构的群胚的相关的稳定图。本文证明了Leavitt路代数$L_Z（E_2）$和$L_Z（E_2-）$不是稳定的 *-同构的。
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.