The graded structure of algebraic Cuntz-Pimsner rings

Abstract

Algebraic Cuntz-Pimsner rings are naturally Z-graded rings that generalize corner skew Laurent polynomial rings, Leavitt path algebras and unperforated Z-graded Steinberg algebras. In this article, we characterize strongly, epsilon-strongly and nearly epsilon-strongly Z-graded algebraic Cuntz-Pimsner rings up to graded isomorphism. We recover two results by Hazrat on when corner skew Laurent polynomial rings and Leavitt path algebras are strongly graded. As a further application, we characterize noetherian and artinian corner skew Laurent polynomial rings.