70 research outputs found
Graphs of quantum groups and K-amenability
No full text38 pagesBuilding on a construction of J-P. Serre, we associate to any graph of C*-algebras a maximal and a reduced fundamental C*-algebra and use this theory to construct the fundamental quantum group of a graph of discrete quantum groups. This construction naturally gives rise to a quantum Bass-Serre tree which can be used to study the K-theory of the fundamental quantum group. To illustrate the properties of this construction, we prove that if all the vertex qantum groups are amenable, then the fundamental quantum group is K-amenable. This generalizes previous results of P. Julg, A. Valette, R. Vergnioux and the first author
A NOTE ON THE VON NEUMANN ALGEBRA OF A BAUMSLAG-SOLITAR GROUP
No full textWe study qualitative properties of the group von Neumann algebra of a Baumslag-Solitar group. Namely, we prove that, in the non-amenable and {ICC} case, the associated factor is prime, not solid, and does not have any Cartan subalgebra
Graphs of quantum groups and K-amenability
No full text38 pagesBuilding on a construction of J-P. Serre, we associate to any graph of C*-algebras a maximal and a reduced fundamental C*-algebra and use this theory to construct the fundamental quantum group of a graph of discrete quantum groups. This construction naturally gives rise to a quantum Bass-Serre tree which can be used to study the K-theory of the fundamental quantum group. To illustrate the properties of this construction, we prove that if all the vertex qantum groups are amenable, then the fundamental quantum group is K-amenable. This generalizes previous results of P. Julg, A. Valette, R. Vergnioux and the first author
A cocycle in the adjoint representation of the orthogonal free quantum groups
No full textInternational audienceWe show that the orthogonal free quantum groups are not inner amenable and we construct an explicit proper cocycle weakly contained in the regular representation. This strengthens the result of Vaes and the second author, showing that the associated von Neumann algebras are full II1-factors and Brannan's result showing that the orthogonal free quantum groups have Haagerup's approximation property. We also deduce Ozawa–Popa's property strong (HH) and give a new proof of Isono's result about strong solidity
Amenable, transitive and faithful actions of groups acting on trees
No full textv.2: minor changes, final version, to appear in Annales de l'Institut FourierWe study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees
Graphs of quantum groups and K-amenability
No full textInternational audienceBuilding on a construction of J.-P. Serre, we associate to any graph of C *-algebras a maximal and a reduced fundamental C *-algebra and use this theory to construct the fundamental quantum group of a graph of discrete quantum groups. This construction naturally gives rise to a quantum Bass-Serre tree which can be used to study the K-theory of the fundamental quantum group. To illustrate the properties of this construction, we prove that if all the vertex quantum groups are amenable, then the fundamental quantum group is K-amenable. This generalizes previous results of P. Julg, A. Valette, R. Vergnioux and the first author. Our proof, even for classical groups, is quite different from the original proof of Julg and Valette, which does not seem to extend straightforwardly to the quantum setting
HNN extensions and unique group measure space decomposition of II1 factors
No full textWe prove that for a fairly large family of HNN extensions Γ, the group measure space II 1 factor L ∞(X) x Γ given by an arbitrary free ergodic probability measure preserving action of Γ has a unique group measure space Cartan subalgebra up to unitary conjugacy. From this we deduce new examples of W*-inferrigid group actions, i.e. where the II1 factor L ∞(X) x Γ entirely remembers the group action from which it was constructed. © 2012 American Mathematical Society.sponsorship: The first author was supported by ERC Starting Grant VNALG-200749. The second author was partially supported by ERC Starting Grant VNALG-200749, Research Programme G.0231.07 of the Research Foundation, Flanders (FWO) and K. U. Leuven BOF research grant OT/08/032. (ERC|VNALG-200749, Research Foundation, Flanders (FWO)|G.0231.07, K. U. Leuven BOF|OT/08/032)status: Publishe
Detection of Eight Periodontal Microorganisms and Distribution of Porphyromonas gingivalis fimA Genotypes in Chinese Patients With Aggressive Periodontitis
No full textBackground: The microbiologic feature of aggressive periodontitis (AgP) in Chinese patients has not yet been determined. This study aims to investigate the prevalence of eight periodontal microorganisms and the distribution of the Porphyromonas gingivalis fimA genotype in a cohort of Chinese patients with AgP. Methods: Saliva and pooled subgingival plaque samples were collected from 81 patients with AgP (25 with incisor-first molar type and 56 with generalized type [GAgP]) and 34 periodontally healthy controls. Eight periodontal microorganisms, including Aggregatibacter actinomycetemcomitans, P. gingivalis, Tannerella forsythia, Treponema denticola, Campylobacter rectus, Prevotella intermedia, Prevotella nigrescens, and Fusobacterium nucleatum were detected in these samples by the polymerase chain reaction (PCR). In addition, the distribution of fimA genotypes was assessed in P. gingivalis-positive individuals by PCR. Results: The prevalence of P. gingivalis, T. forsythia, T. denticola, C. rectus, P. intermedia, F. nucleatum, and A. actinomycetemcomitans in patients with AgP was significantly higher than that in healthy controls. The prevalence of A. actinomycetemcomitans in patients with GAgP was relatively low (30.4%) compared with other pathogens. Results of logistic regression analysis showed that younger patients were more likely to harbor A. actinomycetemcomitans (odds ratio = 2.85). Type II was the most prevalent fimA genotype of P. gingivalis in patients with AgP. Conclusions: P. gingivalis, T. forsythia, T. denticola, C. rectus, P. intermedia, and F. nucleatum were the predominant periodontal pathogens of patients with GAgP in China. Type II of fimA was the most prevalent genotype of P. gingivalis in patients with AgP. The prevalence of A. actinomycetemcomitans in patients with GAgP was relatively low.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000331139400020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Dentistry, Oral Surgery & MedicineSCI(E)[email protected]
K-amenability of HNN extensions of amenable discrete quantum groups
No full textWe construct the HNN extension of discrete quantum groups, we study their representation theory and we show that an HNN extension of amenable discrete quantum groups is K-amenable
Twisting and Rieffel's deformation of locally compact quantum groups. Deformation of the Haar measure.
No full textWe develop the twisting construction for locally compact quantum groups. A new feature, in contrast to the previous work of M. Enock and the second author, is a non-trivial deformation of the Haar measure. Then we construct Rieffel's deformation of locally compact quantum groups and show that it is dual to the twisting. This allows to give new interesting concrete examples of locally compact quantum groups, in particular, deformations of the classical group and of the Woronowicz' quantum group
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