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A Nica-amenable submonoid of a group which fails to embed in an amenable group
Abstract
We construct a weakly quasilattice-ordered submonoid of a group whose full semigroup C*-algebra is nuclear, while the monoid does not embed into any amenable group. Hence, Nica amenability, as well as the nuclearity of its semigroup C*-algebra, do not characterize embeddability into an amenable group for group-embeddable monoids.
Related
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BibTeX
@misc{doron2026nicaamenable,
title = {{A Nica-amenable submonoid of a group which fails to embed in an amenable group}},
author = {Adam Dor-On and Boyu Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12187},
eprint = {2609.12187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12187},
}
RIS
TY - UNPB
TI - A Nica-amenable submonoid of a group which fails to embed in an amenable group
AU - Adam Dor-On
AU - Boyu Li
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12187
UR - https://arxiv.org/abs/2609.12187
AB - We construct a weakly quasilattice-ordered submonoid of a group whose full semigroup C^*-algebra is nuclear, while the monoid does not embed into any amenable group. Hence, Nica amenability, as well as the nuclearity of its semigroup C*-algebra, do not characterize embeddability into an amenable group for group-embeddable monoids.
ER -