% Encoding: UTF-8
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@article{faucris.310441609,
abstract = {In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and obtain an associated structure theorem for asymptotically expanding actions. Based on this, we establish an analytic characterisation for asymptotic expansion in terms of the Druţu–Nowak projection and the Roe algebra of the associated warped cones. As an application, we provide new counterexamples to the coarse Baum–Connes conjecture.},
author = {Li, Kang and Vigolo, Federico and Zhang, Jiawen},
doi = {10.1007/s43037-023-00297-8},
faupublication = {yes},
journal = {Banach Journal of Mathematical Analysis},
keywords = {Asymptotic expansion in measure; Coarse Baum–Connes conjecture; Markov expansion; Spectral gap; Strong ergodicity; Warped cones},
note = {CRIS-Team Scopus Importer:2023-09-15},
peerreviewed = {Yes},
title = {{A} {Markovian} and {Roe}-algebraic approach to asymptotic expansion in measure},
volume = {17},
year = {2023}
}
@article{faucris.265407124,
abstract = {Amenability for groups can be extended to metric spaces, algebras over commutative fields and C^{⁎}-algebras by adapting the notion of Følner nets. In the present article we investigate the close ties among these extensions and show that these three pictures unify in the context of the uniform Roe algebra Cu ^{⁎}(X) over a metric space (X,d) with bounded geometry. In particular, we show that the following conditions are equivalent: (1) (X,d) is amenable; (2) the translation algebra generating Cu ^{⁎}(X) is algebraically amenable (3) Cu ^{⁎}(X) has a tracial state; (4) Cu ^{⁎}(X) is not properly infinite; (5) [1]0≠[0]0 in the K0-group K0(Cu ^{⁎}(X)); (6) Cu ^{⁎}(X) does not contain the Leavitt algebra as a unital ⁎-subalgebra; (7) Cu ^{⁎}(X) is a Følner C^{⁎}-algebra in the sense that it admits a net of unital completely positive maps into matrices which is asymptotically multiplicative in the normalized trace norm. We also show that every possible tracial state of the uniform Roe algebra Cu ^{⁎}(X) is amenable.},
author = {Ara, Pere and Lledo, Fernando and Wu, Jianchao and Li, Kang},
doi = {10.1016/j.jmaa.2017.10.063},
faupublication = {no},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Amenability; Coarse space; Følner conditions; Semi-pre-C; Traces; Uniform Roe algebras},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {686-716},
peerreviewed = {Yes},
title = {{Amenability} and uniform {Roe} algebras},
volume = {459},
year = {2018}
}
@article{faucris.265406627,
abstract = {In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. We apply our general analysis to two important classes of algebras: the unital Leavitt path algebras and the translation algebras on locally finite extended metric spaces. In particular, we show that the amenability of a metric space is equivalent to the algebraic amenability of the corresponding translation algebra.},
author = {Ara, Pere and Lledo, Fernando and Wu, Jianchao and et al.},
author_hint = {Pere Ara, Kang Li, Fernando Lledó, Jianchao Wu},
doi = {10.1007/s13373-017-0109-6},
faupublication = {no},
journal = {Bulletin of Mathematical Sciences},
keywords = {Amenability; Coarse spaces; Følner nets; Leavitt path algebras; Paradoxical decompositions; Translation algebras; Unital K-algebras},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {257-306},
peerreviewed = {Yes},
support_note = {Author relations incomplete. You may find additional data in field 'author{\_}hint'},
title = {{Amenability} of coarse spaces and {K} -algebras},
volume = {8},
year = {2018}
}
@article{faucris.265406122,
abstract = { Very recently, Špakula and Tikuisis provide a new characterisation of (uniform) Roe algebras via quasi-locality when the underlying metric spaces have straight finite decomposition complexity. In this paper, we improve their method to deal with the L ^{p} -version of (uniform) Roe algebras for any p∈[1,∞). Due to the lack of reflexivity on L ^{1} -spaces, some extra work is required for the case of p=1. },
author = {Li, Kang and Wang, Zhijie and Zhang, Jiawen},
doi = {10.1016/j.jmaa.2019.02.013},
faupublication = {no},
journal = {Journal of Mathematical Analysis and Applications},
keywords = { L ; Quasi-local operators; Straight finite decomposition complexity},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {1213-1237},
peerreviewed = {Yes},
title = {{A} quasi-local characterisation of {Lp}-{Roe} algebras},
volume = {474},
year = {2019}
}
@article{faucris.265405118,
abstract = {In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalizes expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterizing strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.},
author = {Li, Kang and Vigolo, Federico and Zhang, Jiawen},
doi = {10.1142/S1793525321500278},
faupublication = {no},
journal = {Journal of Topology and Analysis},
keywords = {asymptotic expanders; Asymptotic expansion in measure; domain of expansion; local spectral gap; strong ergodicity},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {1-39},
peerreviewed = {unknown},
title = {{Asymptotic} expansion in measure and strong ergodicity},
year = {2021}
}
@article{faucris.304999330,
abstract = {Given a commensurated subgroup Λ of a group Γ, we completely characterize when the inclusion Λ ≤ Γ is C*-irreducible and provide new examples of such inclusions. In particular, we obtain that PSL(n, ℤ) ≤ PGL(n,ℚ) is C*-irreducible for any n ∈ ℕ, and that the inclusion of a C*-simple group into its abstract commensurator is C*-irreducible. The main ingredient that we use is the fact that the action of a commensurated subgroup Λ ≤ Γ on its Furstenberg boundary ∂FΛ can be extended in a unique way to an action of Γ on ∂FΛ. Finally, we also investigate the counterpart of this extension result for the universal minimal proximal space of a group.},
author = {Li, Kang and Scarparo, Eduardo},
doi = {10.2140/pjm.2023.322.369},
faupublication = {yes},
journal = {Pacific Journal of Mathematics},
keywords = {C,-simplicity; commensurated subgroups; Furstenberg boundary},
note = {CRIS-Team Scopus Importer:2023-06-09},
pages = {369-380},
peerreviewed = {Yes},
title = {{C}*-{IRREDUCIBILITY} {OF} {COMMENSURATED} {SUBGROUPS}},
volume = {322},
year = {2023}
}
@article{faucris.265406872,
abstract = {We show that for two countable locally finite groups Γ and Λ, the associated uniform Roe algebras Cu*(Γ) and Cu* (Λ) are *-isomorphic if and only if their K0 groups are isomorphic as ordered abelian groups with units. Along the way we obtain a rigidity result: two countable locally finite groups are bijectively coarsely equivalent if and only if the associated uniform Roe algebras are *-isomorphic. We also show that a (not necessarily countable) discrete group Γ is locally finite if and only if the associated uniform Roe algebra ℓ^{∞}(Γ) ⋊r Γ is locally finite-dimensional.},
author = {Li, Kang and Liao, Hung-Chang},
doi = {10.7900/jot.2017may23.2163},
faupublication = {no},
journal = {Journal of Operator Theory},
keywords = {Classification of C*-algebras; Coarse geometry; Uniform Roe algebras},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {25-46},
peerreviewed = {Yes},
title = {{Classification} of uniform {Roe} algebras of locally finite groups},
volume = {80},
year = {2018}
}
@article{faucris.265405367,
abstract = {In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if X and Y are two uniformly locally finite metric spaces such that their Roe algebras are ⁎-isomorphic, then X and Y are coarsely equivalent provided either X or Y satisfies the coarse Baum-Connes conjecture with coefficients. It is well-known that coarse embeddability into a Hilbert space implies the coarse Baum-Connes conjecture with coefficients. On the other hand, we provide a new example of a finitely generated group satisfying the coarse Baum-Connes conjecture with coefficients but which does not coarsely embed into a Hilbert space.},
author = {Braga, Bruno M. and Chung, Yeong Chyuan and Li, Kang},
doi = {10.1016/j.jfa.2020.108728},
faupublication = {no},
journal = {Journal of Functional Analysis},
keywords = {Baum-Connes conjecture; Large scale geometry; Roe algebras},
note = {CRIS-Team Scopus Importer:2021-10-25},
peerreviewed = {Yes},
title = {{Coarse} {Baum}-{Connes} conjecture and rigidity for {Roe} algebras},
volume = {279},
year = {2020}
}
@article{faucris.265404615,
abstract = {We show that the dynamic asymptotic dimension of an action of an infinite virtually cyclic group on a compact Hausdorff space is always one if the action has the marker property. This in particular covers a well-known result of Guentner, Willett, and Yu for minimal free actions of infinite cyclic groups. As a direct consequence, we substantially extend a famous result by Toms and Winter on the nuclear dimension of -algebras arising from minimal free -actions. Moreover, we also prove the marker property for all free actions of countable groups on finite-dimensional compact Hausdorff spaces, generalizing a result of Szabo in the metrisable setting.},
author = {Amini, Massoud and Li, Kang and Sawicki, Damian and Shakibazadeh, Ali},
doi = {10.1017/S0013091521000183},
faupublication = {no},
journal = {Proceedings of the Edinburgh Mathematical Society},
keywords = {dynamic asymptotic dimension; marker property; minimal action; nuclear dimension; virtually cyclic group},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {364-372},
peerreviewed = {Yes},
title = {{Dynamic} asymptotic dimension for actions of virtually cyclic groups},
volume = {64},
year = {2021}
}
@article{faucris.322634224,
abstract = {We introduce higher-dimensional analogs of Kazhdan projections in matrix algebras over group C^{∗}-algebras and Roe algebras. These projections are constructed in the framework of cohomology with coefficients in unitary representations and in certain cases give rise to non-trivial K-theory classes. We apply the higher Kazhdan projections to establish a relation between `2-Betti numbers of a group and surjectivity of different Baum–Connes type assembly maps.},
author = {Li, Kang and Nowak, Piotr W. and Pooya, Sanaz},
doi = {10.4171/JNCG/529},
faupublication = {yes},
journal = {Journal of Noncommutative Geometry},
keywords = {Baum–Connes conjectures; Betti numbers; Kazhdan projections; Roe algebras},
note = {CRIS-Team Scopus Importer:2024-05-17},
pages = {313-336},
peerreviewed = {Yes},
title = {{Higher} {Kazhdan} projections, `2-{Betti} numbers and {Baum}–{Connes} conjectures},
volume = {18},
year = {2024}
}
@article{faucris.265405871,
abstract = {In this paper, we study the ideal structure of reduced -algebras associated to étale groupoids . In particular, we characterize when there is a one-to-one correspondence between the closed, two-sided ideals in and the open invariant subsets of the unit space of . As a consequence, we show that if is an inner exact, essentially principal, ample groupoid, then is (strongly purely infinite if and only if every non-zero projection in is properly infinite in . We also establish a sufficient condition on the ample groupoid that ensures pure infiniteness of in terms of paradoxicality of compact open subsets of the unit space . Finally, we introduce the type semigroup for ample groupoids and also obtain a dichotomy result: let be an ample groupoid with compact unit space which is minimal and topologically principal. If the type semigroup is almost unperforated, then is a simple -algebra which is either stably finite or strongly purely infinite.},
author = {Boenicke, Christian and Li, Kang},
doi = {10.1017/etds.2018.39},
faupublication = {no},
journal = {Ergodic Theory and Dynamical Systems},
month = {Jan},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {34-63},
peerreviewed = {Yes},
title = {{Ideal} structure and pure infiniteness of ample groupoid {C}∗-algebras},
volume = {40},
year = {2020}
}
@article{faucris.265407376,
abstract = {The goal of this paper is to study when uniform Roe algebras have certain Cz.ast; - -algebraic properties in terms of the underlying space: in particular, we study properties like having stable rank one or real rank zero that are thought of as low dimensional, and connect these to low dimensionality of the underlying space in the sense of the asymptotic dimension of Gromov. Some of these results (for example, on stable rank one, cancellation, strong quasidiagonality, and finite decomposition rank) give definitive characterizations, while others (on real rank zero) are only partial and leave a lot open. We also establish results about K-theory, showing that all K0-classes come from the inclusion of the canonical Cartan in low-dimensional cases, but not in general; in particular, our K-theoretic results answer a question of Elliott and Sierakowski about vanishing of K0 groups for uniform Roe algebras of non-amenable groups. Along the way, we extend some results about paradoxicality, proper infiniteness of projections in uniform Roe algebras, and supramenability from groups to general metric spaces. These are ingredients needed for our K-theoretic computations, but we also use them to give new characterizations of supramenability for metric spaces.},
author = {Li, Kang and Willett, Rufus},
doi = {10.1112/jlms.12100},
faupublication = {no},
journal = {Journal of the London Mathematical Society-Second Series},
keywords = {20F69; 46L05; 46L80; 46L85; 55M10 (primary)},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {98-124},
peerreviewed = {Yes},
title = {{Low}-dimensional properties of uniform {Roe} algebras},
volume = {97},
year = {2018}
}
@article{faucris.282438222,
abstract = {In this paper, we give a new geometric condition in terms of measured asymptotic expanders to ensure rigidity of Roe algebras. Consequently, we obtain the rigidity for all bounded geometry spaces that coarsely embed into some L-p-space for p is an element of [1, infinity). Moreover, we also verify rigidity for the box spaces constructed by Arzhantseva-Tessera and Delabie-Khukhro even though they do not coarsely embed into any L-p-space. The key step in our proof of rigidity is showing that a block-rank-one (ghost) projection on a sparse space X belongs to the Roe algebra C*(X) if and only if X consists of (ghostly) measured asymptotic expanders. As a by-product, we also deduce that ghostly measured asymptotic expanders are new sources of counterexamples to the coarse Baum-Connes conjecture.},
author = {Li, Kang and Spakula, Jan and Zhang, Jiawen},
doi = {10.1093/imrn/rnac242},
faupublication = {yes},
journal = {International Mathematics Research Notices},
note = {CRIS-Team WoS Importer:2022-09-30},
peerreviewed = {Yes},
title = {{Measured} {Asymptotic} {Expanders} and {Rigidity} for {Roe} {Algebras}},
year = {2022}
}
@article{faucris.282048355,
abstract = {By measured graphs, we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincare inequalities. We prove that the so-called Cheeger inequality holds in two cases: when the measure comes from a random walk, or when the measure has a bounded measure ratio. Moreover, we also prove that our measured (asymptotic) expanders are generalised expanders introduced by Tessera. Finally, we present some examples to demonstrate relations and differences between classical expander graphs and the measured ones. This paper is motivated primarily by our previous work on the rigidity problem for Roe algebras.},
author = {Li, Kang and Spakula, Jan and Zhang, Jiawen},
doi = {10.1142/S1793525322500078},
faupublication = {yes},
journal = {Journal of Topology and Analysis},
note = {CRIS-Team WoS Importer:2022-09-23},
peerreviewed = {Yes},
title = {{Measured} expanders},
year = {2022}
}
@article{faucris.325116471,
abstract = {In this paper, we study almost finiteness and almost finiteness in measure of nonfree actions. Let (Formula presented.) be a minimal action of a locally finite-by-virtually (Formula presented.) group (Formula presented.) on the Cantor set (Formula presented.). We prove that under certain assumptions, the action (Formula presented.) is almost finite in measure if and only if (Formula presented.) is essentially free. As an application, we obtain that any minimal topologically free action of a virtually (Formula presented.) group on an infinite compact metrizable space with the small boundary property is almost finite. This is the first general result, assuming only topological freeness, in this direction, and these lead to new results on uniform property (Formula presented.) and (Formula presented.) -stability for their crossed product (Formula presented.) -algebras. Some concrete examples of minimal topological free (but nonfree) subshifts are provided.},
author = {Li, Kang and Ma, Xin},
doi = {10.1112/jlms.12959},
faupublication = {yes},
journal = {Journal of the London Mathematical Society-Second Series},
note = {CRIS-Team Scopus Importer:2024-07-05},
peerreviewed = {Yes},
title = {{Nonfree} almost finite actions for locally finite-by-virtually {Z} groups},
volume = {110},
year = {2024}
}
@article{faucris.298207141,
abstract = {We investigate the notion of tracial Z-stability beyond unital C-algebras, and we prove that this notion is equivalent to Z-stability in the class of separable simple nuclear C-algebras.},
author = {Castillejos, J. O.R.G.E. and Li, Kang and Szabó, Gabor},
doi = {10.4153/S0008414X23000202},
faupublication = {yes},
journal = {Canadian Journal of Mathematics-Journal Canadien De Mathematiques},
note = {CRIS-Team Scopus Importer:2023-04-28},
peerreviewed = {Yes},
title = {{ON} {TRACIAL}-{Z}-{STABILITY} of {SIMPLE} {NON}-{UNITAL} {C}∗-{ALGEBRAS}},
year = {2023}
}
@article{faucris.265404867,
abstract = {In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some C *-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.},
author = {Li, Kang and Nowak, Piotr and Spakula, Jan and Zhang, Jiawen},
doi = {10.4171/GGD/610},
faupublication = {no},
journal = {Groups Geometry and Dynamics},
keywords = {Expanders; Nuclearity; Property A; Quasi-local algebras},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {655-682},
peerreviewed = {Yes},
title = {{Quasi}-local algebras and asymptotic expanders},
volume = {15},
year = {2021}
}
@article{faucris.265406374,
abstract = {We investigate the rigidity of the (Formula presented.) analog of Roe-type algebras. In particular, we show that if (Formula presented.), then an isometric isomorphism between the (Formula presented.) uniform Roe algebras of two metric spaces with bounded geometry yields a bijective coarse equivalence between the underlying metric spaces, while a stable isometric isomorphism yields a coarse equivalence. We also obtain similar results for other (Formula presented.) Roe-type algebras. In this paper, we do not assume that the metric spaces have Yu's property A or finite decomposition complexity.},
author = {Chung, Yeong Chyuan and Li, Kang},
doi = {10.1112/blms.12201},
faupublication = {no},
journal = {Bulletin of the London Mathematical Society},
keywords = {46H15 (secondary); 46H20 (primary); 46L85; 51K05},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {1056-1070},
peerreviewed = {Yes},
title = {{Rigidity} of ℓp {Roe}-type algebras},
volume = {50},
year = {2018}
}
@article{faucris.265405619,
abstract = {In this paper we show that for an almost finite minimal ample groupoid G, its reduced C^{∗}-algebra Cr∗(G) has real rank zero and strict comparison even though Cr∗(G) may not be nuclear in general. Moreover, if we further assume G being also second countable and non-elementary, then its Cuntz semigroup Cu(Cr∗(G)) is almost divisible and Cu(Cr∗(G)) and Cu(Cr∗(G)⊗Z) are canonically order-isomorphic, where Z denotes the Jiang-Su algebra.},
author = {Ara, Pere and Bonicke, Christian and Bosa, Joan and Li, Kang},
doi = {10.1007/s43037-020-00079-6},
faupublication = {no},
journal = {Banach Journal of Mathematical Analysis},
keywords = {Almost finite groupoids; Cuntz semigroups; Strict comparison},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {1692-1710},
peerreviewed = {Yes},
title = {{Strict} comparison for {C}∗ -algebras arising from almost finite groupoids},
volume = {14},
year = {2020}
}
@article{faucris.275325107,
abstract = {We introduce the Haagerup property for twisted groupoid C*-dynamical systems in terms of naturally defined positive definite operator-valued multipliers. By developing a version of 'the Haagerup trick' we prove that this property is equivalent to the Haagerup property of the reduced crossed product C*-algebra with respect to the canonical conditional expectation E. This extends a theorem of Dong and Ruan for discrete group actions, and implies that a given Cartan inclusion of separable C*-algebras has the Haagerup property if and only if the associated Weyl groupoid has the Haagerup property in the sense of Tu. We use the latter statement to prove that every separable C*-algebra which has the Haagerup property with respect to some Cartan subalgebra satisfies the Universal Coefficient Theorem. This generalises a recent result of Barlak and Li on the UCT for nuclear Cartan pairs. (C) 2022 Elsevier Inc. All rights reserved.},
author = {Kwasniewski, Bartosz K. and Li, Kang and Skalski, Adam},
doi = {10.1016/j.jfa.2022.109484},
faupublication = {yes},
journal = {Journal of Functional Analysis},
note = {CRIS-Team WoS Importer:2022-05-20},
peerreviewed = {Yes},
title = {{The} {Haagerup} property for twisted groupoid dynamical systems},
volume = {283},
year = {2022}
}
@article{faucris.265407629,
abstract = {The main purpose of this paper is to modify the orbit method for the Baum-Connes conjecture as developed by Chabert, Echterhoff and Nest in their proof of the Connes-Kasparov conjecture for almost connected groups (Chabert J., S. Echterhoff, and R. Nest, The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups, Publ. Math. Inst. Hautes Études Sci., 97 (2003), 239-278) in order to deal with linear algebraic groups over local function fields (i.e., non-archimedean local fields of positive characteristic). As a consequence, we verify the Baum-Connes conjecture for certain Levi-decomposable linear algebraic groups over local function fields. One of these is the Jacobi group, which is the semidirect product of the symplectic group and the Heisenberg group.},
author = {Echterhoff, Siegfried and Nest, Ryszard and Li, Kang},
faupublication = {no},
journal = {Journal of Lie Theory},
keywords = {Baum-Connes conjecture; Linear algebraic groups; Local function fields; Orbit method},
note = {CRIS-Team Scopus Importer:2021-10-25},
pages = {323-341},
peerreviewed = {Yes},
title = {{The} orbit method for the {Baum}-{Connes} conjecture for algebraic groups over local function fields},
volume = {28},
year = {2018}
}
@article{faucris.277346527,
abstract = {In this paper, we show that every separable simple tracially approximately divisible (Formula presented.) -algebra has strict comparison, and it is either purely infinite or has stable rank one. As a consequence, we show that every (non-unital) finite simple (Formula presented.) -stable (Formula presented.) -algebra has stable rank one.},
author = {Fu, Xuanlong and Li, Kang and Lin, Huaxin},
doi = {10.1112/jlms.12654},
faupublication = {yes},
journal = {Journal of the London Mathematical Society-Second Series},
note = {CRIS-Team Scopus Importer:2022-07-01},
peerreviewed = {Yes},
title = {{Tracial} approximate divisibility and stable rank one},
year = {2022}
}