## Amenability and functoriality of right-LCM semigroup C*-algebras

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- by Marcelo Laca and Boyu Li
- Proc. Amer. Math. Soc.
**148**(2020), 5209-5224 - DOI: https://doi.org/10.1090/proc/15139
- Published electronically: September 4, 2020
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## Abstract:

We prove a functoriality result for the full C*-algebras of right-LCM monoids with respect to monoid inclusions that are closed under factorization and preserve orthogonality, and use this to show that if a right-LCM monoid is amenable in the sense of Nica, then so are its submonoids. As applications, we complete the classification of Artin monoids with respect to Nica amenability by showing that only the right-angled ones are amenable in the sense of Nica and we show that the Nica amenability of a graph product of right-LCM semigroups having no nontrivial units is inherited by the factors.## References

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## Bibliographic Information

**Marcelo Laca**- Affiliation: Department of Mathematics and Statistics, University of Victoria, PO Box 1700 STN CSC, Victoria, B.C., Canada V8W 2Y2
- MR Author ID: 335785
- Email: laca@uvic.ca
**Boyu Li**- Affiliation: Department of Mathematics and Statistics, University of Victoria, PO Box 1700 STN CSC, Victoria, B.C., Canada V8W 2Y2
- MR Author ID: 1169918
- ORCID: 0000-0003-2484-1851
- Email: boyuli@uvic.ca
- Received by editor(s): January 13, 2020
- Received by editor(s) in revised form: March 30, 2020, and April 13, 2020
- Published electronically: September 4, 2020
- Additional Notes: The second author was supported by a fellowship from the Pacific Institute for the Mathematical Sciences.
- Communicated by: Adrian Ioana
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 5209-5224 - MSC (2010): Primary 46L05; Secondary 20F36, 47D03
- DOI: https://doi.org/10.1090/proc/15139
- MathSciNet review: 4163833