40 research outputs found
HAAGERUP APPROXIMATION PROPERTY VIA BIMODULES
No full textThe Haagerup approximation property (HAP) is defined for finite von Neumann algebras in such a way that the group von Neumann algebra of a discrete group has the HAP if and only if the group itself has the Haagerup property. The HAP has been studied extensively for finite von Neumann algebras and it was recently generalized to arbitrary von Neumann algebras by Caspers-Skalski and Okayasu-Tomatsu. One of the motivations behind the generalization is the fact that quantum group von Neumann algebras are often infinite even though the Haagerup property has been defined successfully for locally compact quantum groups by Daws-Fima-Skalski-White. In this paper, we fill this gap by proving that the von Neumann algebra of a locally compact quantum group with the Haagerup property has the HAP. This is new even for genuine locally compact groups
Quasicentral approximate units relative to the Macaev norm (The structure of operator algebras and its applications)
No full textHaagerup approximation property via bimodules
No full textThe Haagerup approximation property (HAP) is defined for finite von Neumann algebras in such a way that the group von Neumann algebra of a discrete group has the HAP if and only if the group itself has the Haagerup property. The HAP has been studied extensively for finite von Neumann algebras and it was recently generalized to arbitrary von Neumann algebras by Caspers-Skalski and Okayasu-Tomatsu. One of the motivations behind the generalization is the fact that quantum group von Neumann algebras are often infinite even though the Haagerup property has been defined successfully for locally compact quantum groups by Daws-Fima-Skalski-White. In this paper, we fill this gap by proving that the von Neumann algebra of a locally compact quantum group with the Haagerup property has the HAP. This is new even for genuine locally compact groups
Quasicentral Approximate Units and Finitely Generated Groups (Quantum Analysis in Operator Algebras)
No full textCuntz-Krieger-Pimsner Algebras Associated with Amalgamated Free Products Groups (Free products in operator algebras and related topics)
No full textGénéralisations de la propriété d'approximation de Haagerup pour les algèbres de von Neumann arbitraires
No full textThe notion of the Haagerup approximation property, originally introduced for von Neumann algebras equipped with a faithful normal tracial state, is generalised to arbitrary von Neumann algebras. We discuss two equivalent characterisations, one in term of the standard form and the other in term of the approximating maps with respect to a fixed faithful normal semifinite weight. Several stability properties, in particular regarding the crossed product construction are established and certain examples are introduced.La notion de propriété d'approximation de Haagerup, introduite à l'origine pour les algèbres de von Neumann ayant une trace finie, normale, et fidèle, est généralisée pour les algèbres de von Neumann arbitraires. Nous discutons deux caractérisations équivalentes : une du point de vue de la représentation standard et une autre du point de vue des applications linéaires approximantes liées à un poids fidèle, normal, semifini. Quelques propriétés de permanence, en particulier celles concernant les produits croisés, sont établies et certains exemples sont introduits
Petersenidia leleji Williams & Lelej & Okayasu & Borkent & Malee & Thoawan & Thaochan 2019, sp. nov.
No full text27b. <i>Petersenidia leleji</i> Williams, sp. nov. <p>(Figs 143–144)</p> <p> <b>Diagnosis.</b> FEMALE. The following combination of characters is diagnostic: humeral angle weakly produced, pronotum broader than propodeum, mesosoma uniform orange, legs partly orange, metasoma entirely black, T2 sculpture weak, T2 disc spots small and separated by ~3 × spot diameter, T2 with sparse white apical fringe, T3 band entire, and pygidium smooth. Body length 5.4 mm. MALE. Unknown.</p> <p> <b>Description.</b> FEMALE. Body length 5.4 mm. <i>Coloration.</i> Head black, except antennal tubercle, mandible, scape, and clypeus largely red-brown, and venter of flagellum largely orange-brown. Mesosoma, coxae, and femoral bases orange-brown, femoral apices, tibiae, and tarsi blackish. Metasoma black, except T1, S1, and T6 largely red-brown. Body setae generally sparse and silvery, except frons, vertex, and mesosomal dorsum with suberect blackish and red-brown setae; T2 disc, T4, and T5 setae dense black; and T2 disc lateral spots, T3 entirely, and T6 basal tuft with dense whitish-silver setae; T2 lateral spot diameter 0.3 × distance between spots, T2 with sparse apical fringe of pale silvery setae, and T3 band entire. <i>Head</i>. Width behind eye 0.9 × mesosoma width. Frons, vertex, and gena punctures dense to confluent. Mandible apex apparently unidentate. Clypeus apically bidentate, teeth connected by transverse carina; basomedial portion with robust tubercle. Antennal scrobe with arcuate dorsal carina and straight lateral carina. Antennal tubercle with scattered micropunctures. Genal carina weak, forming small tooth at hypostomal carina and extending posteriorly to occipital carina. F1 2.0 × pedicel length, F2 1.5 × pedicel length. <i>Mesosoma</i>. Length subequal to width. Dorsum of mesosoma with coarse confluent punctures; obscure interrupted carina separating dorsal and lateral faces of pronotum and mesonotum. Side of mesosoma with dense micropunctures and short setae. Mesopleural lamella an obscure carina. Humeral carina weak, complete. Ratio of width of humeral angle, anterior spiracle, narrowest point of mesonotum, propodeal spiracle, and midpoint of propodeum 70:78:70:72:73. Scutellar scale rounded posteriorly, ~2 punctures wide. Posterior propodeal face reticulate with many interspaces obliterated leaving apparent striae. Lateral and posterior propodeal faces separated by wavy carina with few short teeth. Metatibio-tarsal ratio 58:24:13:10:9:10. <i>Metasoma.</i> T1 anterior face with sparse punctures, posterior with confluent punctures. T2 disc with moderate separated pits, interspaces micropunctate and setose; with obscure transverse depression in apical half. T3–5 and S3–5 with small dense punctures. S1 with simple longitudinal lamella. S2 with sparse punctures, interspaces smooth. T2 felt line 0.3 × T2 total length. T6 with long sub-ovate pygidium, widest medially with lateral carina obliterated in posterior half; smooth throughout. S6 posterior margin truncate.</p> <p> <b>Material examined. Holotype ♀,</b> THAILAND, <i>Phatthalung</i>, 2.4 km S Ban Na, Farm, 7.543 o N 99.883 o E, 50 m, 6.IV.2017, MKT (CSCA). <b>Paratypes (22 ♀),</b> THAILAND, <i>Chiang Mai</i>, Doi Ang Khang, 1300 m, 21.VIII.1998 (1♀ SKYC). VIETNAM: <i>Vinh Phu</i>, Tam Dao, forest, 10–15.XI.1990, S. Belokobylskij (5♀ ZISP, IBSS); <i>Ha Son Binh</i>: Da Bac, Tuly, fores, 22–23.X.1990, S. Belokobylskij (2♀ ZISP); Mai Chou, forest, 3. XI.1 990, S. Belokobylskij (12♀ ZISP); <i>Hoa Binh,</i> Mai Chau, Pa Co Xa Linh, 20°44'N 104°55'E, 1120 m, 22–24.IV.2002, S. Belokobylskij (1♀ ZISP); <i>Quang Ninh</i>, Baitu Long Islands, Dong Ho Il., 20.III.1987, V. Kuznetsov (1♀ IBSS).</p> <p> <b>Distribution.</b> Thailand (Chiang Mai, Phatthalung), Vietnam (Ha Son Binh, Hoa Binh, Quang Ninh, Vinh Phu).</p> <p> <b>Etymology.</b> KAW is happy to name this species for his co-author and friend, Arkady Lelej, for his contributions to this and many other mutillid research projects.</p> <p> <b>Remarks.</b> In Chen’s (1957) key, this species terminates at couplet 7 of the <i>Smicromyrme</i> key, because the pygidium is smooth and the S1 carina is entire. In Mickel’s (1935) key, it terminates at couplet 9 because the antenna is largely orange-brown and the genal punctures are moderately large.</p>Published as part of <i>Williams, Kevin A., Lelej, Arkady S., Okayasu, Juriya, Borkent, Christopher J., Malee, Rufeah, Thoawan, Kodeeyah & Thaochan, Narit, 2019, The female velvet ants (aka modkhong) of southern Thailand (Hymenoptera: Mutillidae), with a key to the genera of southeast Asia, pp. 1-69 in Zootaxa 4602 (1)</i> on pages 40-41, DOI: <a href="http://zenodo.org/record/2669927">10.5281/zenodo.2669927</a>
-algebras associated with the fundamental groups of graphs of groups
No full textWe construct a nuclear -algebra associated with the fundamental group of a graph of groups of finite type. It is well-known that every word-hyperbolic group with zero-dimensional boundary, in other words, every group acting trees with finite stabilizers is given by the fundamental group of such a graph of groups. We show that our -algebra is -isomorphic to the crossed product arising from the associated boundary action and is also given by a Cuntz-Pimsner algebra. We also compute the K-groups and determine the ideal structures of our -algebras
Cuntz-Krieger-Pimsner Algebras Associated with Amalgamated Free Product Groups
No full textWe give a construction of a nuclear C*-algebra associated with an amalgamated free product of groups, generalizing Spielberg's construction of a certain Cuntz- Krieger algebra associated with a finitely generated free product of cyclic groups. Our nuclear C*-algebras can be identified with certain Cuntz-Krieger-Pimsner algebras. We will also show that our algebras can be obtained by the crossed product construction of the canonical actions on the hyperbolic boundaries, which proves a special case of Adams' result about amenability of the boundary action for hyperbolic groups. We will also give an explicit formula of the K-groups of our algebras. Finally we will investigate a relationship between the KMS states of the generalized gauge actions on our C*-algebras and random walks on the groups
A note on injective factors with trivial bicentralizer
No full textWe give an alternative proof that an injective factor on a Hilbert space with
trivial bicentralizer is ITPFI. Our proof is given in parallel with each type
of factors and it is based on the strategy of Haagerup. As a consequence, the
uniqueness theorem of injective factors except type III follows from
Araki-Woods' result.Comment: The paper will appear in the Publications of Research Institute for
Mathematical Sciences, Kyoto Universit
