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

Published online by Cambridge University Press:  25 January 2023

Thomas Gotfredsen
Roskilde Business College, Bakkesvinget 67, 4000 Roskilde, Denmark e-mail:
Sophie Emma Zegers*
Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 186 75 Praha 8, Czech Republic


We investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline {m}))$ , introduced by Brzeziński and Szymański as graph $C^*$ -algebras. We give a new description of $C(L_q^{2n+1}(r;\underline {m}))$ as graph $C^*$ -algebras amending an error in the original paper by Brzeziński and Szymański. Furthermore, 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 Sørensen.

© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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This work was supported by the DFF-Research Project 2 on “Automorphisms and invariants of operator algebras” (Grant No. 7014–00145B). The second author was moreover supported by the Carlsberg Foundation through an Internationalisation Fellowship.


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