$\mathbb{Z}$-graded rings as Cuntz-Pimsner rings

Lisa Orloff Clark; James Fletcher; Roozbeh Hazrat; Huanhuan Li

$\mathbb{Z}$-graded rings as Cuntz-Pimsner rings

Rings and Algebras 2018-11-06 v2 Operator Algebras

Authors: Lisa Orloff Clark , James Fletcher , Roozbeh Hazrat , Huanhuan Li

Abstract

Given a $\mathbb{Z}$ -graded ring $A$ and a subring $R\subseteq A$ , it is natural to ask whether $A$ can be realised as the Cuntz-Pimsner ring of some $R$ -system. In this paper, we derive sufficient conditions on $A$ and $R$ for this to be the case. As an application, we give conditions under which the Steinberg algebra $A_K(\mathcal{G})$ associated to a $\mathbb{Z}$ -graded groupoid $\mathcal{G}=\sqcup_{n\in \mathbb{Z}} \mathcal{G}_n$ can be realised as the Cuntz-Pimsner ring of an $A_K(\mathcal{G}_0)$ -system.

Keywords

commutative ring theory graded algebras

Cite

@article{arxiv.1808.10114,
  title  = {$\mathbb{Z}$-graded rings as Cuntz-Pimsner rings},
  author = {Lisa Orloff Clark and James Fletcher and Roozbeh Hazrat and Huanhuan Li},
  journal= {arXiv preprint arXiv:1808.10114},
  year   = {2018}
}

Comments

16 pages, fixed a small number of typographical errors. arXiv admin note: text overlap with arXiv:0810.3254 by other authors

$\mathbb{Z}$-graded rings as Cuntz-Pimsner rings

Abstract

Keywords

Cite

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