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The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous
Abstract
The Motzkin subproduct system (SPS) is constructed from the Jones Wenzl idempotents of the Motzkin algebras, which generalizes the Temperley Lieb SPS. The simplest Motzkin SPS, which is not a Temperley Lieb SPS, is constructed from a 3 dimensional Hilbert space. We explicitly describe the spectrum of the corresponding Cuntz Pimsner algebra, which remarkably admits only irreducible representations of dimensions 1 and 2, and can thus be viewed as a mildly quantum space. We moreover analyse representations of the Richard Thompson groups and of the Cuntz algebra that are associated to this spectrum.
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BibTeX
@misc{aiello2026cuntzpimsner,
title = {{The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous}},
author = {Valeriano Aiello and Arnaud Brothier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.10349},
eprint = {2609.10349},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10349},
}
RIS
TY - UNPB
TI - The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous
AU - Valeriano Aiello
AU - Arnaud Brothier
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.10349
UR - https://arxiv.org/abs/2609.10349
AB - The Motzkin subproduct system (SPS) is constructed from the Jones Wenzl idempotents of the Motzkin algebras, which generalizes the Temperley Lieb SPS. The simplest Motzkin SPS, which is not a Temperley Lieb SPS, is constructed from a 3 dimensional Hilbert space. We explicitly describe the spectrum of the corresponding Cuntz Pimsner algebra, which remarkably admits only irreducible representations of dimensions 1 and 2, and can thus be viewed as a mildly quantum space. We moreover analyse representations of the Richard Thompson groups and of the Cuntz algebra that are associated to this spectrum.
ER -