Fourier algebras of certain connected groups are not projective

Oleg, Aristov,

doi:10.1070/rm2005v060n01abeh000811

Cited by 2 publications

(3 citation statements)

References 2 publications

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“…But E was also a right ⊳-module map, which implies that E R is a left ⊲-module map by the generalized antipode relation (3). Thus, we also have…”

Section: Proposition 52 Let G Be a Locally Compact Group Then L 1 mentioning

confidence: 82%

“…The averaging argument used above, together with its variants used in [3,14], shows that it is inner amenability, as opposed to discreteness, that underlies the original averaging technique of Haagerup. In the setting of unimodular discrete quantum groups G, the technique relies on the existence of a normal left inverse Φ : [23,Theorem 7.5] and [41,Theorem 5.5]).…”

Section: By Strict Continuity and The Definition Of The Multiplicatio...mentioning

confidence: 99%

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Inner amenability and approximation properties of locally compact quantum groups

Crann¹

2019

Indiana Univ. Math. J.

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We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological properties of the dual quantum group, which allow us to generalize a well-known result of Lau-Paterson [46], resolve a recent conjecture of Ng-Viselter [51], and prove that, for inner amenable quantum groups G, approximation properties of the dual operator algebras can be averaged to approximation properties of G. Similar homological techniques are used to prove that ℓ 1 (G) is not relatively operator biflat for any non-unimodular discrete quantum group G; a unimodular discrete quantum group G with Kirchberg's factorization property is weakly amenable if and only if L 1 cb ( G) is operator amenable, and amenability of a locally compact quantum group G implies Cu( G) ∼ = L 1 ( G) ⊗ L 1 ( G) C0( G) completely isometrically. The latter result allows us to partially answer a conjecture of Voiculescu [67] when G has the approximation property.2010 Mathematics Subject Classification. Primary 22D35; Secondary 46M10, 46L89.

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“…But E was also a right ⊳-module map, which implies that E R is a left ⊲-module map by the generalized antipode relation (3). Thus, we also have…”

Section: Proposition 52 Let G Be a Locally Compact Group Then L 1 mentioning

confidence: 82%

Section: By Strict Continuity and The Definition Of The Multiplicatio...mentioning

confidence: 99%

Inner amenability and approximation properties of locally compact quantum groups

Crann¹

2019

Indiana Univ. Math. J.

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“…On the other hand, Aristov observed that there are connected groups whose Fourier algebras are not operator projective over itself. In particular, G = SL(3, R) is such an example [3]. Unfortunately, at this point there is no obvious conjecture as to when A(G) is operator projective in A(G)-mod.…”

Section: Operator Projectivity Of A(g)mentioning

confidence: 99%

Projectivity of modules over Fourier algebras

Forrest

Lee

Samei

2010

Proceedings of the London Mathematical Society

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In this paper we study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we focus on the question of identifying when such modules are projective in the category of operator spaces. We will show that projectivity often implies that the underlying group is discrete and give evidence to show that amenability also plays an important role.

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Fourier algebras of certain connected groups are not projective

Cited by 2 publications

References 2 publications

Inner amenability and approximation properties of locally compact quantum groups

Inner amenability and approximation properties of locally compact quantum groups

Projectivity of modules over Fourier algebras

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