Vol. 297, No. 2, 2018

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Combinatorial classification of quantum lens spaces

Peter Lunding Jensen, Frederik Ravn Klausen and Peter M. R. Rasmussen

Vol. 297 (2018), No. 2, 339–365
Abstract

We answer the question of how large the dimension of a quantum lens space must be, compared to the primary parameter r, for the isomorphism class to depend on the secondary parameters. Since classification results in C-algebra theory reduce this question to one concerning a certain kind of SL-equivalence of integer matrices of a special form, our approach is entirely combinatorial and based on the counting of certain paths in the graphs shown by Hong and Szymański to describe the quantum lens spaces.

Keywords
quantum lens space, C*-algebra, SL equivalence
Mathematical Subject Classification 2010
Primary: 46L35
Secondary: 05C30
Milestones
Received: 16 January 2017
Revised: 19 April 2018
Accepted: 20 April 2018
Published: 20 December 2018
Authors
Peter Lunding Jensen
Department of Mathematical Sciences
University of Copenhagen
Denmark
Frederik Ravn Klausen
Department of Mathematical Sciences
University of Copenhagen
Denmark
Peter M. R. Rasmussen
Department of Mathematical Sciences
University of Copenhagen
Denmark