Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Authors: Marcelo Laca and Boyu Li
Journal: Proc. Amer. Math. Soc. 148 (2020), 5209-5224
MSC (2010): Primary 46L05; Secondary 20F36, 47D03
DOI: https://doi.org/10.1090/proc/15139
Published electronically: September 4, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L05, 20F36, 47D03

Retrieve articles in all journals with MSC (2010): 46L05, 20F36, 47D03


Additional 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

DOI: https://doi.org/10.1090/proc/15139
Keywords: Right-LCM semigroup, amenable, Artin monoid
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
Article copyright: © Copyright 2020 American Mathematical Society