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

Part of: Infinite-dimensional manifolds Selfadjoint operator algebras Graph theory

Published online by Cambridge University Press:  25 January 2023

Thomas Gotfredsen Open the ORCID record for Thomas Gotfredsen[Opens in a new window]  and
Sophie Emma Zegers Open the ORCID record for Sophie Emma Zegers[Opens in a new window]
Thomas Gotfredsen
Affiliation:
Roskilde Business College, Bakkesvinget 67, 4000 Roskilde, Denmark e-mail: tgo@rhs.dk gotfredsen_thomas@hotmail.com
Sophie Emma Zegers*
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 186 75 Praha 8, Czech Republic
*
e-mail: zegers@karlin.mff.cuni.cz sophieemmazegers@gmail.com
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Abstract

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.

Keywords

Graph C *-algebrasclassificationquantum lens spaces

MSC classification

Primary: 46L35: Classifications of $C^*$-algebras 58B34: Noncommutative geometry (à la Connes)
Secondary: 05C30: Enumeration in graph theory
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 37
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

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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