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

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 is inherited by the factors.

Left regular representations of Garside categories I. C*-algebras and groupoids

“…Our contribution concerns the remaining cases. We can also characterise when C * λ (P) or Ker ∂ is nuclear (see also [38,Theorem 4.2]). Moreover, we point out that K-theory for semigroup C * -algebras of Artin-Tits monoids has been computed in [44], assuming that the corresponding Artin-Tits group satisfies the Baum-Connes conjecture with coefficients.…”