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

Laca, Marcelo; Li, Boyu

doi:10.1090/proc/15139

Amenability and functoriality of right-LCM semigroup C*-algebras
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Proc. Amer. Math. Soc. 148 (2020), 5209-5224 Request permission

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.

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