On the classification and description of quantum lens spaces as graph algebras

Abstract

We investigate quantum lens spaces, C(L 2n+1 q (r; m)), introduced by Brzeziński-Szymański as graph C * -algebras. We give a new description of C(L 2n+1 q (r; m)) as graph C * -algebras amending an error in the original paper by Brzeziński-Szymański. Furthermore, for n ≤ 3, we give a number-theoretic invariant, when all but one weight are coprime to the order of the acting group r. This builds upon the work of Eilers, Restorff, Ruiz and Sørensen.