Z-graded rings as Cuntz–Pimsner rings

• DOI: 10.1016/j.jalgebra.2019.07.012
• Publication Date: 2019-07-22T23:29:58Z
• Authors: Lisa Orloff Clark; James Fletcher; Roozbeh Hazrat; Huanhuan Li
• Keywords: graded rings; groupoids; 010101 - Algebra and Number Theory; algebra; 0101 mathematics; 01 natural sciences

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 A K ( G ) associated to a Z -graded groupoid G = ⊔ n ∈ Z G n can be realised as the Cuntz–Pimsner ring of an A K ( G 0 ) -system.