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arXiv · 2609.12187

A Nica-amenable submonoid of a group which fails to embed in an amenable group

Adam Dor-On·Boyu Li
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Abstract

We construct a weakly quasilattice-ordered submonoid of a group whose full semigroup $\mathrm{C}^*$-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.

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Adam Dor-On, Boyu Li. 2026-09-10. A Nica-amenable submonoid of a group which fails to embed in an amenable group. https://arxiv.org/abs/2609.12187

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