Notes on treeability and costs for discrete groupoids in operator algebra framework
算子代数
2019-05-21 v4 动力系统
摘要
We provide an operator algebraic interpretation of discrete measurable groupoids in the course of re-proving (and slightly generalizing) a result on treeability due to Adams and Spatzier. Then, we reconstruct Gaboriau's beautiful work on costs of equivalence relations in operator algebra framework, avoiding any measure theoretic argument, and clarify what kind of his results can or cannot be generalized to the non-principal groupoid case.
引用
@article{arxiv.math/0504262,
title = {Notes on treeability and costs for discrete groupoids in operator algebra framework},
author = {Yoshimichi Ueda},
journal= {arXiv preprint arXiv:math/0504262},
year = {2019}
}
备注
These notes are partly from the lectures we gave at University of Tokyo in Fall, 2004. Minor typos are corrected (June/4/05)