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

Abstract

AbstractWe investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline {m}))$ , introduced by Brzeziński and Szymański as graph $C^*$ -algebras. We give a new description of $C(L_q^{2n+1}(r;\underline {m}))$ as graph $C^*$ -algebras amending an error in the original paper by Brzeziński and Szymański. Furthermore, for $n\leq 3$ , 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.