A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras

Lisa Orloff Clark; Ruy Exel; Enrique Pardo

A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras

Rings and Algebras 2016-09-12 v1 Operator Algebras

Authors: Lisa Orloff Clark , Ruy Exel , Enrique Pardo

Abstract

Given an ample, Hausdorff groupoid $\mathcal{G}$ , and a unital commutative ring $R$ , we consider the Steinberg algebra $A_R(\mathcal {G})$ . First we prove a uniqueness theorem for this algebra and then, when $\mathcal{G}$ is graded by a cocycle, we study graded ideals in $A_R(\mathcal {G})$ . Applications are given for two classes of ample groupoids, namely those coming from actions of groups on graphs, and also to groupoids defined in terms of Boolean dynamical systems.

Keywords

Steinberg algebra uniqueness theorem graded ideal ample groupoid cocycle Boolean dynamical system

Cite

@article{arxiv.1609.02873,
  title  = {A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras},
  author = {Lisa Orloff Clark and Ruy Exel and Enrique Pardo},
  journal= {arXiv preprint arXiv:1609.02873},
  year   = {2016}
}

A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras

Abstract

Keywords

Cite

Related papers