Quasi-symmetric group algebras and C*-completions of Hecke algebras

Palma, Rui

doi:10.48550/arxiv.1210.3807

Cited by 2 publications

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“…An even stronger question, posed in [9], is still open: if C * (G, Γ) exists, does it necessarily follow that C * (G, Γ) ∼ = C * (L 1 (G, Γ)) ∼ = pC * (G)p ? Many of the new classes studied in this article will be shown in a following article (see [16]) to have this property.…”

Section: G Is Locally-finite and γ Is Finitementioning

confidence: 81%

“…Some of the new results we prove state that if a group G satisfies some generalized nilpotency property, then for any Hecke subgroup Γ the Hecke algebra H(G, Γ) has an enveloping C * -algebra which coincides with C * (L 1 (G, Γ)). These results will enable us to show, in a following article (see [16]), that for any G satisfying such properties, Hall's correspondence holds for any Hecke subgroup.…”

Section: Introductionmentioning

confidence: 85%

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On enveloping C*-algebras of Hecke algebras

Palma

2012

Preprint

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We give a sufficient condition for a * -algebra with a specified basis to have an enveloping C * -algebra. Particularizing to the setting of a Hecke algebra H(G, Γ), we show that under a suitable assumption not only we can assure that an enveloping C * -algebra C * (G, Γ) exists, but also that it coincides with C * (L 1 (G, Γ)), the enveloping C * -algebra of the L 1 -Hecke algebra. Our methods are used to show the existence of C * (G, Γ) and isomorphism with C * (L 1 (G, Γ)) for several classes of Hecke algebras. Most of the classes which are known to satisfy these properties are covered by this approach, and we also describe some new ones.

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Section: G Is Locally-finite and γ Is Finitementioning

confidence: 81%

Section: Introductionmentioning

confidence: 85%

On enveloping C*-algebras of Hecke algebras

Palma

2012

Preprint

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“…These questions have already been asked by the author in [13], and the groups in questions 1) and 2) are natural to be considered in this regard.…”

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confidence: 99%

On the growth of Hermitian groups

Palma¹

2015

Groups Geom. Dyn.

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A locally compact group G is said to be Hermitian if every selfadjoint element of L 1 (G) has real spectrum. Using Halmos' notion of capacity in Banach algebras and a result of Jenkins, Fountain, Ramsay and Williamson we will put a bound on the growth of Hermitian groups. In other words, we will show that if G has a subset that grows faster than a certain constant, then G cannot be Hermitian. Our result allows us to give new examples of non-Hermitian groups which could not tackled by the existing theory. The examples include certain infinite free Burnside groups, automorphism groups of trees, and p-adic general and special linear groups.

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Quasi-symmetric group algebras and C*-completions of Hecke algebras

Cited by 2 publications

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On enveloping C*-algebras of Hecke algebras

On enveloping C*-algebras of Hecke algebras

On the growth of Hermitian groups

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