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Non-Supramenable Groups Acting On Locally Compact Spaces

Publications associées (38)

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Sesquilinear forms over rings with involution

Eva Bayer Fluckiger, Daniel Arnold Moldovan

Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cance ...

Elsevier2014

L-2-Betti numbers and Plancherel measure

Henrik Densing Petersen, Alain Valette

We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...

Academic Press Inc Elsevier Science2014

AN OBSTRUCTION TO l(p)-DIMENSION

Nicolas Monod, Henrik Densing Petersen

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 obst ...

Annales Inst Fourier2014

Brace Bar-Cobar Duality

Justin Robert Young

Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) \Omega ...

2013

On the multi-Koszul property for connected algebras.

In this article we introduce the notion of emphmulti-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous ...

2013

Fixed points and amenability in non-positive curvature

Nicolas Monod

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...

Springer2013

Cantor systems, piecewise translations and simple amenable groups

Nicolas Monod

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 suita ...

Annal Mathematics2013

On the topological full group of a minimal Cantor Z2-system

Nicolas Monod, Gábor Elek

Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor Z-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the negative by prod ...

2013

Normal generation of locally compact groups

Nicolas Monod, Amichai Netanel Eisenmann

It is a well-known open problem since the 1970s whether a finitely generated perfect group can be normally generated by a single element or not. We prove that the topological version of this problem has an affirmative answer as long as we exclude infinite ...

Oxford Univ Press2013

Lattice theoretic approach to space-time codes from division algebras

Cyril Becker

This master project on algebraic coding theory gathers various techniques from lattice theory, central simple algebras and algebraic number theory. The thesis begins with the formulation of the engineering problem into mathematical form. It presents how sp ...

2012