Publication

AN OBSTRUCTION TO l(p)-DIMENSION

Nicolas Monod, Henrik Densing Petersen
2014
Journal Articles

Résumé

Let G be any group containing an infinite elementary amenable subgroup and let 2 < p < infinity. We construct an exhaustion of l(p) G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to l(p)-dimension and gives an answer to a question of Gaboriau.

Source officielle

https://infoscience.epfl.ch/entities/publication/ea71503c-c0bf-4edd-b57e-f8875da80400

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Nicolas Monod, Henrik Densing Petersen
2014
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/ea71503c-c0bf-4edd-b57e-f8875da80400

À propos de ce résultat

Concepts associés (7)

Elementary amenable group

In mathematics, a group is called elementary amenable if it can be built up from finite groups and abelian groups by a sequence of simple operations that result in amenable groups when applied to amenable groups. Since finite groups and abelian groups are amenable, every elementary amenable group is amenable - however, the converse is not true.

Groupe moyennable

En mathématiques, un groupe moyennable (parfois appelé groupe amenable par calque de l'anglais) est un groupe topologique localement compact qu'on peut munir d'une opération de « moyenne » sur les fonctions bornées, invariante par les translations par les éléments du groupe. La définition initiale, donnée à partir d'une mesure (simplement additive) des sous-ensembles du groupe, fut proposée par John von Neumann en 1929 à la suite de son analyse du paradoxe de Banach-Tarski.

Linear group

In mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K). Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class.

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Publications associées (12)

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An upper bound for the Tarski numbers of nonamenable groups of piecewise projective homeomorphisms

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The Tarski number of a nonamenable group is the smallest number of pieces needed for a paradoxical decomposition of the group. Nonamenable groups of piecewise projective homeomorphisms were introduced in [N. Monod, Groups of piecewise projective homeomorph ...

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Representing groups against all odds

Maxime Gheysens

We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...

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