Z-graded rings as Cuntz-Pimsner rings

JOURNAL OF ALGEBRA

卷:536

Article

Clark, Lisa Orloff¹  Fletcher, James¹  Hazrat, Roozbeh²  Li, Huanhuan² 

[1] Victoria Univ Wellington, Sch Math & Stat, POB 600, Wellington 6140, New Zealand

[2] Western Sydney Univ, Ctr Res Math, Sydney, NSW, Australia

关键词: Cuntz-Pimsner rings;    Steinberg algebras;    Graded rings;    Groupoid algebras;   

DOI  :  10.1016/j.jalgebra.2019.07.012

来源: Elsevier

【 摘 要 】

Given a Z-graded ring A and a subring R subset of 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)(G) associated to a Z-graded groupoid G = coproduct(n is an element of Z)G(n) can be realised as the Cuntz-Pimsner ring of an A(K) (G(0))-system. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free