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

2022/02/01 by Gotfredsen, Thomas, Zegers, Sophie Emma
#05C30 #46L35 #58B34 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2202.00400

Abstract

We investigate quantum lens spaces, C(L_q²ⁿ⁺¹(r;\underlinem)), introduced by Brzeziński-Szymański as graph C^*-algebras. We give a new description of C(L_q²ⁿ⁺¹(r;\underlinem)) as graph C^*-algebras amending an error in the original paper by Brzeziński-Szymański. 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.

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