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Phases in the cyclic quantum dilogarithm: correction to "Cyclic quantum Teichmüller theory"
Abstract
We first correct μN-phase issues in the basic definition around the cyclic quantum dilogarithm operators in [Ish26]. In particular, the notion of global coefficients must be extended by incorporating additional lifting data forming a μN-cover, and the pentagon relation generally acquires an extra μN-factor. Nevertheless, we prove that every point in a regular locus of the partially compactified cluster Poisson variety lifts to a \emph{strict} extended global coefficient, for which this extra μN-factor is trivial. Consequently, the original statements of [Ish26] hold for such lifts and are therefore restored.
Related
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BibTeX
@misc{ishibashi2026phases,
title = {{Phases in the cyclic quantum dilogarithm: correction to "Cyclic quantum Teichmüller theory"}},
author = {Tsukasa Ishibashi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23572},
eprint = {2610.23572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23572},
}
RIS
TY - UNPB
TI - Phases in the cyclic quantum dilogarithm: correction to "Cyclic quantum Teichmüller theory"
AU - Tsukasa Ishibashi
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23572
UR - https://arxiv.org/abs/2610.23572
AB - We first correct μ_N-phase issues in the basic definition around the cyclic quantum dilogarithm operators in [Ish26]. In particular, the notion of global coefficients must be extended by incorporating additional lifting data forming a μ_N-cover, and the pentagon relation generally acquires an extra μ_N-factor. Nevertheless, we prove that every point in a regular locus of the partially compactified cluster Poisson variety lifts to a \emph{strict} extended global coefficient, for which this extra μ_N-factor is trivial. Consequently, the original statements of [Ish26] hold for such lifts and are therefore restored.
ER -