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

TL;DR

This paper classifies quantum lens spaces of dimension up to 7 using a new number-theoretic invariant, extending previous work on their algebraic structure and providing insights into their classification.

Contribution

It introduces a novel number-theoretic invariant for quantum lens spaces of dimension up to 7, specifically when all but one weight are coprime to the group order.

Findings

Classification achieved for dimensions up to 7.

New invariant distinguishes quantum lens spaces.

Builds on prior algebraic classification methods.

Abstract

We investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline{m}))$, introduced by Brzezi\'nski-Szyma\'nski as graph $C^*$-algebras. 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 S\{o}rensen.