On The Classification of Quantum Lens Spaces of Dimension at most 7

Abstract

We investigate quantum lens spaces, C(L 2n+1 q (r; m)), introduced by Brzeziński-Szymański as graph C * -algebras. 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.

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

“…Then we deal with classification of quantum lens spaces of dimension at most 7, with certain conditions on their weights. We remark that the work on classification has already been presented in an earlier preprint, unpublished, available on arXiv, [18], by the present authors. After the submission of the preprint to arXiv it was pointed out the the authors by Efren Ruiz that the graph C * -algebraic description of quantum lens spaces is incorrect in some cases.…”

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

“…Then we deal with classification of quantum lens spaces of dimension at most 7, with certain conditions on their weights. We remark that the work on classification has already been presented in an earlier preprint, unpublished, On the classification and description of quantum lens spaces as graph algebras 247 available on arXiv [18] by the present authors. After the submission of the preprint to arXiv, it was pointed out by Efren Ruiz that the graph C * -algebraic description of quantum lens spaces is incorrect in some cases.…”