HNN extensions of von Neumann algebras

Ueda, Yoshimichi

doi:10.1016/j.jfa.2005.01.004

Cited by 21 publications

(16 citation statements)

References 38 publications

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“…To prove that M is prime, we use the HNN construction in the framework of von Neumann algebras and we refer to [Ue04,Ue07,FV10] Observe that we cannot directly use Theorem E to get that M is prime, as the inclusion N ⊕ N ⊂ M 2 (N ) has a trivial corner. We already showed however that M is a nonamenable factor.…”

Section: Applications To Amalgamated Free Products Vonmentioning

confidence: 99%

Type III factors with unique Cartan decomposition

Houdayer

Vaes

2013

Journal de Mathématiques Pures et Appliquées

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Abstract. We prove that for any free ergodic nonsingular nonamenable action Γ (X, µ) of all Γ in a large class of groups including all hyperbolic groups, the associated group measure space factor L ∞ (X) ⋊ Γ has L ∞ (X) as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in [PV12]. We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products M1 * B M2 over a subalgebra B of type I.

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Section: Applications To Amalgamated Free Products Vonmentioning

confidence: 99%

Type III factors with unique Cartan decomposition

Houdayer

Vaes

2013

Journal de Mathématiques Pures et Appliquées

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“…The maximal (or full, or universal) HNN extension was also introduced in [Ue05]. We keep the same notations as before and we still assume that we have conditional expectations with faithful G.N.S.…”

Section: The Maximal Hnn Extensionmentioning

confidence: 99%

“…The name HNN is given in honor to G. Higman, B. H. Neuman and H. Neumann who were the first authors to consider this construction in [HNN49]. This construction was developed by Ueda [Ue05] in the setting of von Neumann algebras and C * -algebras. Another approach was given by the author and S. Vaes [FV12] in the setting of tracial von Neumann algebras.…”

Section: Introductionmentioning

confidence: 99%

K -amenability of HNN extensions of amenable discrete quantum groups

Fima

2013

Journal of Functional Analysis

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“…Assume furthermore that there exists a conditional expectation of A i over B such that the GNS representation is strongly injective. Following [2], we can show: Because of Ueda's remark [5], Theorem 3.1 has an immediate application to HNN extensions as follows.…”

Section: Free Product Of K-cycles and Applicationsmentioning

confidence: 97%

KK-theory for some graph C⁎-algebras

Germain

Sarr

2015

Comptes Rendus. Mathématique

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In [2], the first author had presented a method to obtain a K-equivalence between full and reduced free products of nuclear unital C * -algebras. The object of this note is to show how it can be extended to free products with amalgamation over a finite dimensional algebra. As a consequence the K-equivalence holds for graph-C * -algebras whose edge stabilizers are all finite dimensional.© 2015 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. r é s u m é Dans [2], le premier auteur avait présenté une méthode pour obtenir l'équivalence en K-théorie entre les produits libres pleins ou réduits de C * -algèbres nucléaires unifères. Nous montrons ici comment étendre ce résultat aux produits libres amalgamés au-dessus d'une algèbre de dimension finie. Ceci permet alors de démontrer le même type de résultat pour les graphes d'algèbres quand les stabilisateurs des arêtes sont de dimension finie.

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HNN extensions of von Neumann algebras

Cited by 21 publications

References 38 publications

Type III factors with unique Cartan decomposition

Type III factors with unique Cartan decomposition

K -amenability of HNN extensions of amenable discrete quantum groups

KK-theory for some graph C⁎-algebras

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