40 citations · 183 across the 41 of their papers we have counts for
36 papers · 1 filter
Stable isomorphisms of operator algebras
Evgenios Kakariadis, Elias Katsoulis, Xin Li
Let $\A$ and $\B$ be operator algebras with -isomorphic diagonals and let $\K$ denote the compact operators. We show that if $\A\otimes\K$ and $\B\otimes\K$ are isometrically…
Algebraic actions I. C*-algebras and groupoids
Chris Bruce, Xin Li
We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce…
Constructing C*-diagonals in AH-algebras
Xin Li, Ali Imad Raad
We construct Cartan subalgebras and hence groupoid models for classes of AH-algebras. Our results cover all AH-algebras whose building blocks have base spaces of dimension at most…
Semigroup C*-algebras arising from graphs of monoids
Cheng Chen, Xin Li
We study groupoids and semigroup C*-algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gi…
Left regular representations of Garside categories II. Finiteness properties of topological full groups
Xin Li
We study topological full groups attached to groupoid models for left regular representations of Garside categories. Groups arising in this way include Thompson's group and man…
Left regular representations of Garside categories I. C*-algebras and groupoids
Xin Li
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…
Co-universality and controlled maps on product systems over right LCM-semigroups
Evgenios T. A. Kakariadis, Elias G. Katsoulis, Marcelo Laca +1
We study the structure of C*-algebras associated with compactly aligned product systems over group embeddable right LCM-semigroups. Towards this end we employ controlled maps and a…
The ideal intersection property for essential groupoid C*-algebras
Matthew Kennedy, Se-Jin Kim, Xin Li +2
We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C*-algebra has the ideal intersection propert…
Boundary quotient C*-algebras of semigroups
Evgenios T. A. Kakariadis, Elias G. Katsoulis, Marcelo Laca +1
We study two classes of operator algebras associated with a unital subsemigroup of a discrete group : one related to universal structures, and one related to co-universal st…
C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems
Adam Dor-On, Evgenios T. A. Kakariadis, Elias G. Katsoulis +2
A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly speak…
Constructing Menger manifold C*-diagonals in classifiable C*-algebras
Xin Li
We construct C*-diagonals with connected spectra in all classifiable stably finite C*-algebras which are unital or stably projectionless with continuous scale. For classifiable sta…
K-theory for semigroup C*-algebras and partial crossed products
Xin Li
Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly --unitary inverse semigroups, or equivalently, for certa…
Operator algebras of higher rank numerical semigroups
Evgenios T. A. Kakariadis, Elias G. Katsoulis, Xin Li
A higher rank numerical semigroup is a positive cone whose seminormalization is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint semigroup algebras are kn…
C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type
Xin Li, Tron Omland, Jack Spielberg
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 nucle…
Every classifiable simple C*-algebra has a Cartan subalgebra
Xin Li
We construct Cartan subalgebras in all classifiable stably finite C*-algebras. Together with known constructions of Cartan subalgebras in all UCT Kirchberg algebras, this shows tha…
Semigroup C*-algebras
Xin Li
We give an overview of some recent developments in semigroup C*-algebras.
Cartan subalgebras and the UCT problem, II
Selcuk Barlak, Xin Li
We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding cross…
Cartan subalgebras in C*-algebras. Existence and uniqueness
Xin Li, Jean Renault
We initiate the study of Cartan subalgebras in C*-algebras, with a particular focus on existence and uniqueness questions. For homogeneous C*-algebras, these questions can be analy…
Partial transformation groupoids attached to graphs and semigroups
Xin Li
We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crosse…
The isomorphism problem for semigroup C*-algebras of right-angled Artin monoids
Søren Eilers, Xin Li, Efren Ruiz
Semigroup C*-algebras for right-angled Artin monoids were introduced and studied by Crisp and Laca. In the paper at hand, we are able to present the complete answer to their questi…
A new approach to recent constructions of C*-algebras from modular index theory
Xin Li
We present a new approach to C*-algebras recently constructed in the context of modular index theory by Carey, Phillips, Putnam and Rennie. It turns out that their constructions ca…
Independent resolutions for totally disconnected dynamical systems II: C*-algebraic case
Xin Li, Magnus Dahler Norling
We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution…
Semigroup C*-algebras of -semigroups
Xin Li
We study semigroup C*-algebras of -semigroups over integral domains. The goal is to generalize several results about C*-algebras of -semigroups over rings of algebraic…
On K-theoretic invariants of semigroup C*-algebras attached to number fields
Xin Li
We show that semigroup C*-algebras attached to ax+b-semigroups over rings of integers determine number fields up to arithmetic equivalence, under the assumption that the number fie…