On The Classification and Description of Quantum Lens Spaces as Graph algebras

Abstract

. We investigate quantum lens spaces, C ( L 2 n +1 q ( r ; m )), introduced by Brzezi´nski-Szyma´nski as graph C ∗ -algebras. We give a new description of C ( L 2 n +1 q ( r ; m )) as graph C ∗ -algebras amending an error in the original paper by Brzezi´nski-Szyma´nski. 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.