In this work we introduce and study a new notion of amenability for actions of locally
compact groups on $ C^* $-algebras. Our definition extends the definition of amenability for …

To each submonoid $ P $ of a group we associate a universal Toeplitz $\mathrm {C}^* $-
algebra $\mathcal {T} _u (P) $ defined via generators and relations; $\mathcal {T} _u (P) $ is …

Let P be a submonoid of a group G and let E=(E p) p∈ P be a product system over P with
coefficient C⁎-algebra A. We show that the following C⁎-algebras are canonically …

A discrete countable group G is matricially stable if the finite dimensional approximate
unitary representations of G are perturbable to genuine representations in the point-norm …

We show that a normal coaction of a discrete group on an operator algebra extends to a
normal coaction on the C*-envelope. This resolves an open problem considered by …

We initiate the study of C*-algebras and groupoids arising from left regular representations
of Garside categories, a notion which originated from the study of Braid groups. Every higher …

This is a survey article about recent developments in semigroup C*-algebras. These C*-
algebras generated by left regular representations of semigroups have been studied for …

Given a right LCM semigroup SS and a homomorphism N: S→ 1,+∞) N:S→1,+∞), we use
the groupoid approach to study the KMS β _β‐states on C∗(S) C^*(S) with respect to the …

Abstract Using the Baum–Connes conjecture with coefficients, we develop a K-theory
formula for reduced C*-algebras of strongly 0-E-unitary inverse semigroups, or equivalently …

We study C*-algebras generated by left regular representations of right LCM one-relator
monoids and Artin–Tits monoids of finite type. We obtain structural results concerning …