Publication

Cantor systems, piecewise translations and simple amenable groups

Nicolas Monod
2013
Journal Articles

Résumé

We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space.

Source officielle

https://infoscience.epfl.ch/entities/publication/a6eb8223-fbc7-4ba2-b455-66a39a2f5199

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Nicolas Monod
2013
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/a6eb8223-fbc7-4ba2-b455-66a39a2f5199

À propos de ce résultat

Concepts associés (19)

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.

Thompson groups

In mathematics, the Thompson groups (also called Thompson's groups, vagabond groups or chameleon groups) are three groups, commonly denoted , that were introduced by Richard Thompson in some unpublished handwritten notes in 1965 as a possible counterexample to the von Neumann conjecture. Of the three, F is the most widely studied, and is sometimes referred to as the Thompson group or Thompson's group. The Thompson groups, and F in particular, have a collection of unusual properties that have made them counterexamples to many general conjectures in group theory.

Groupe simple

En mathématiques, un groupe simple est un groupe non trivial qui ne possède pas de sous-groupe distingué autre que lui-même et son sous-groupe trivial. Un groupe est dit simple s'il a exactement deux sous-groupes distingués : ( étant l’élément neutre du groupe) et lui-même. Quelques exemples de groupes simples : Les seuls groupes abéliens simples sont les groupes finis d'ordre premier (ces groupes sont cycliques). Le groupe SO_3(R) des matrices spéciales orthogonales d'ordre 3 à coefficients réels est simple.

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Approximating nonabelian free groups by groups of homeomorphisms of the real line

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Simple groups of birational transformations in dimension two

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We classify simple groups that act by birational transformations on compact complex Kahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrar ...

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