Simple reduced $L^p$-operator crossed products with unique trace

Hejazian, Shirin; Pooya, Sanaz

doi:10.7900/jot.2014may13.2036

Cited by 13 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, it is easy to see that the classical condition to have infinite (non-trivial) conjugacy classes characterises factoriality of group convolution algebras on arbitrary r -spaces. Moreover, the articles [HP15;Phi19] show that also on a C * -algebraic level, simplicity of a classical operator algebra associated with a group implies simplicity of its r -analogues. Our result shows that for Hecke operator algebras a similar implication holds no longer true.…”

Section: Introductionmentioning

confidence: 99%

Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings

Raum¹,

Skalski²

2020

Preprint

View full text Add to dashboard Cite

We obtain a complete characterisation of factorial multiparameter Hecke von Neumann algebras associated with right-angled Coxeter groups. Considering their p -convolution algebra analogues, we exhibit an interesting parameter dependence, contrasting phenomena observed earlier for group Banach algebras. Translated to Iwahori-Hecke von Neumann algebras, these results allow us to draw conclusions on spherical representation theory of groups acting on right-angled buildings, which are in strong contrast to behaviour of spherical representations in the affine case. We also investigate certain graph product representations of right-angled Coxeter groups and note that our von Neumann algebraic structure results show that these are finite factor representations. Further classifying them up to unitary equivalence allows us to reveal high-dimensional Euclidean subspaces of the space of extremal characters of right-angled Coxeter groups.

show abstract

Section: Introductionmentioning

confidence: 99%

Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings

Raum¹,

Skalski²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In 2012 and 2013, Phillips [51], [52], [53] introduced L p versions of some C * -algebra notions including UHF algebras and Cuntz algebras. See [25], [26], [32] [24], [27], [54] for some results in this direction. Most of the results about algebras of operators on L p that appear in the literature are in the "isometric theory," i.e., the "isomorphisms" (in the sense of category theory) between algebras of operators on L p are the isometric isomorphisms.…”

Section: Introductionmentioning

confidence: 99%

Similarity of operators on $l^{p}$

Boedihardjo

2017

Preprint

View full text Add to dashboard Cite

We prove a version of each of the following results for operators on l p , 1 < p < ∞: (i) Voiculescu's absorption theorem (ii) that Ext(C(M )) is a group for every nonempty compact subset M of R d (iii) that Ext(A) −1 is homotopy invariant in A for separable unital C * -algebra A. Contents 1. Introduction 1 2. l p version of Voiculescu's theorem 8 3. Proof of the l p version of Voiculescu's theorem 9 4. Consequences of the l p version of Voiculescu's theorem 22 5. Isomorphic extensions of K(l p ) by C * -algebras 30 6. Ext ∼ s,r (C(M ), K(l p )) is a group 39 7. Homotopy invariance of Ext ∼ s,r (A, K(l p )) −1 52 8. Open problems 75 References 76 2010 Mathematics Subject Classification. 47A65.

show abstract

“…As a corollary, we get the following theorem. Theorem 3.6(1) implies group algebra case (but not the general statement for crossed products) in Theorem 3.5 of [6].…”

mentioning

confidence: 98%

Simplicity of reduced group Banach algebras

Phillips

2019

Preprint

View full text Add to dashboard Cite

Let G be a discrete group. Suppose that the reduced group C*algebra C * r (G) is simple. We use results of Kalantar-Kennedy and Haagerup, and Banach space interpolation, to prove that, for p ∈ (1, ∞), the reduced group L p operator algebra F p r (G) and its *-analog B p, * r (G) are simple. If G is countable, we prove that the Banach algebras generated by the left regular representations on reflexive Orlicz sequence spaces and certain Lorentz sequence spaces are also simple. We prove analogous results with simplicity replaced by the unique trace property. For use in the Orlicz sequence space case, we prove that if p ∈ (1, ∞), then any reflexive Orlicz sequence space is isomorphic (not necessarily isometrically) to a space gotten by interpolation between l p and some other Orlicz sequence space.

show abstract

Simple reduced $L^p$-operator crossed products with unique trace

Cited by 13 publications

References 14 publications

Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings

Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings

Similarity of operators on $l^{p}$

Simplicity of reduced group Banach algebras

Contact Info

Product

Resources

About