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

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