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-Szymański as graph $C^{\ast }$-algebras. We give a new description of $C(L_q^{2n+1}(r;\underline{m}))$ as graph $C^{\ast }$-algebras amending an error in the original paper by Brzeziński-Szymański. Furthermore, for $n\le 3$, 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.

arXiv admin note: substantial text overlap with arXiv:2104.06137