Z-graded rings as Cuntz-Pimsner rings

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

doi:10.1016/j.jalgebra.2019.07.012

Z-graded rings as Cuntz-Pimsner rings

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

Western Sydney University

Research output: Contribution to journal › Article › peer-review

Abstract

Given a Z-graded ring A and a subring R⊆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 AK(G) associated to a Z-graded groupoid G=⊔n∈ZGn can be realised as the Cuntz–Pimsner ring of an AK(G0)-system.

Original language	English
Pages (from-to)	82-101
Number of pages	20
Journal	Journal of Algebra
Volume	536
DOIs	https://doi.org/10.1016/j.jalgebra.2019.07.012
Publication status	Published - 2019

Keywords

algebra
graded rings
groupoids

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10.1016/j.jalgebra.2019.07.012

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title = "Z-graded rings as Cuntz-Pimsner rings",

abstract = "Given a Z-graded ring A and a subring R⊆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 AK(G) associated to a Z-graded groupoid G=⊔n∈ZGn can be realised as the Cuntz–Pimsner ring of an AK(G0)-system.",

keywords = "algebra, graded rings, groupoids",

author = "Clark, {Lisa Orloff} and James Fletcher and Roozbeh Hazrat and Huanhuan Li",

year = "2019",

doi = "10.1016/j.jalgebra.2019.07.012",

language = "English",

volume = "536",

pages = "82--101",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press",

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T1 - Z-graded rings as Cuntz-Pimsner rings

AU - Clark, Lisa Orloff

AU - Fletcher, James

AU - Hazrat, Roozbeh

AU - Li, Huanhuan

PY - 2019

Y1 - 2019

N2 - Given a Z-graded ring A and a subring R⊆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 AK(G) associated to a Z-graded groupoid G=⊔n∈ZGn can be realised as the Cuntz–Pimsner ring of an AK(G0)-system.

AB - Given a Z-graded ring A and a subring R⊆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 AK(G) associated to a Z-graded groupoid G=⊔n∈ZGn can be realised as the Cuntz–Pimsner ring of an AK(G0)-system.

KW - algebra

KW - graded rings

KW - groupoids

UR - https://hdl.handle.net/1959.7/uws:54491

U2 - 10.1016/j.jalgebra.2019.07.012

DO - 10.1016/j.jalgebra.2019.07.012

M3 - Article

SN - 0021-8693

VL - 536

SP - 82

EP - 101

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Z-graded rings as Cuntz-Pimsner rings

Abstract

Keywords

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