Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Dor-On, Adam, Li, Boyu
Institutions: New Mexico State University, University of Haifa
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: NSF-BSF: Semigroup Operator Algebras - Representations, Boundaries and Dynamics, Gruppoidmodelle für Diagramme von Gruppoidkorrespondenzen und ihre C*Algebren, Collaborative Research: NSF-BSF - Dynamics Through the Viewpoint of Self-Similar Algebras: Topological Markov Chains and Self-Similar Groups.
OpenAlex ID: W7212480947