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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 ...
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 ...
Using the Riemann Hypothesis over finite fields and bounds for the size of spherical codes, we give explicit upper bounds, of polynomial size with respect to the size of the field, for the number of geometric isomorphism classes of geometrically irreducibl ...
We theoretically investigated the symmetry properties of the modes in two-dimensional square lattice photonic crystals in order to study phenomena that would enable new frontiers in the applications of photonic crystals. Using group theory, symmetry analys ...
A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...
The results of a group theoretical analysis of the excitonic fine structure are presented and compared with spectroscopic data on single quantum dots. The spectral features reveal the signatures of a symmetry higher than the crystal symmetry (C-3v). A cons ...
Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust mes- sage-passing schemes for distributed information processing over networks. However, for many topologies that are realistic for wire- less ...
Institute of Electrical and Electronics Engineers2010
A general formalism for the maximal symmetrization and reduction of fields (MSRFs) is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and ...
J.Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Fur ...
