Rigidity theory for C∗C^*-dynamical systems and the "Pedersen Rigidity Problem", II

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen's theorem, which does hold for an arbitrary locally compact group $G$, saying that two actions $(A,\alpha)$ and $(B,\beta)$ of $G$ are outer conjugate if and only if the dual coactions $(A\rtimes_{\alpha}G,\widehat\alpha)$ and $(B\rtimes_{\beta}G,\widehat\beta)$ of $G$ are conjugate via an isomorphism that maps the image of $A$ onto the image of $B$ (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images, and we have decided to use the term "Pedersen rigid" for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call "fixed-point rigidity". In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known.Comment: Minor revision. To appear in Internat. J. Mat

Cuntz-Li algebras from a-adic numbers

The a-adic numbers are those groups that arise as Hausdorff completions of noncyclic subgroups of the rational numbers. We give a crossed product construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers and investigate the structure of the associated algebras. In particular, these algebras are in many cases Kirchberg algebras in the UCT class. Moreover, we prove an a-adic duality theorem, which links a Cuntz-Li algebra with a corresponding dynamical system on the real numbers. The paper also contains an appendix where a nonabelian version of the "subgroup of dual group theorem" is given in the setting of coactions.Comment: 41 pages; revised versio

Strong Pedersen rigidity for coactions of compact groups

We prove a version of Pedersen's outer conjugacy theorem for coactions of compact groups, which characterizes outer conjugate coactions of a compact group in terms of properties of the dual actions. In fact, we show that every isomorphism of a dual action comes from a unique outer conjugacy of a coaction, which in this context should be called strong Pedersen rigidity. We promote this to a category equivalence.Comment: 13 pages. Minor revision, with numerous wording changes but the same theorems. To appear in IJ

In-water synthesis of isocyanides under micellar conditions

An in-water dehydration of N-formamides to afford isocyanides using micellar conditions at room temperature is reported. This method allows for the preparation of aliphatic isocyanides in an environmental friendly manner. The replacement of undesirable components such as phosphorous oxychloride, triethyl amine and dichloromethane (the classical combination used for the dehydration of N-formamides), by p-toluen sulphonyl chloride, sodium hydrogen carbonate and water makes this transformation really sustainable and safe

Deformations of Gabor frames on the adeles and other locally compact abelian groups

We generalize Feichtinger and Kaiblinger's theorem on linear deformations of uniform Gabor frames to the setting of a locally compact abelian group $G$. More precisely, we show that Gabor frames over lattices in the time-frequency plane of $G$ with windows in the Feichtinger algebra are stable under small deformations of the lattice by an automorphism of ${G}\times \widehat{G}$. The topology we use on the automorphisms is the Braconnier topology. We characterize the groups in which the Balian-Low theorem for the Feichtinger algebra holds as exactly the groups with noncompact identity component. This generalizes a theorem of Kaniuth and Kutyniok on the zeros of the Zak transform on locally compact abelian groups. We apply our results to a class of number-theoretic groups, including the adele group associated to a global field.Comment: 37 page

M004 In aortic stenosis, 2D speckle tracking differentiates left ventricular dysfunction load- to remodelling-dependant

BackgroundIn aortic stenosis, it is not known which between longitudinal, radial and circumferential contraction is influenced by loading conditions or remodelling. To test our hypothesis and to understand left ventricular function recovery, we investigated patients at early, i.e. 7 days (contractility enhancement load-dependant) and at late follow-up, i.e. 3 months (contractility enhancement remodelling-dependant) after transcutaneous aortic valve implantation (TAVI).Methods and ResultsTwenty-three subjects (AS: valve orifice < or =0.7cm2; 14 female; mean age, 84+/-6 years) were studied. All subjects of the study had conventional 2D-Doppler echocardiography and speckle tracking analysis (GE HealthCare). Speckle tracking was sampled in short-axis view for radial and circumferential strain and in apical 4, 3 and 2-chamber view for averaged longitudinal strain. Measurements were performed before, 7 days and 3 months after TAVI. Mean pressure gradient decreased from 41±20mmHg to 10±3mmHg (p<0.001) while aortic valve area increased from 0.6±0.1 to 1.7±0.2cm2 (p<0.001) after implantation. Biplane Simpson EF was 50±10 %, 51±13 and 58±11 % at baseline, 7-day and 3-month follow-up (p=0.01), respectively. Improvement of circumferential strain found 7 days after TAVI is sustained at 3 months. Radial strain increased shortly after TAVI, then decreased at 3 months and was compensated by improvement of longitudinal strain (see figure).ConclusionIn patients with aortic stenosis, radial contraction is load dependant, circumferential contraction is both load- and remodelling-dependant, whereas longitudinal contraction is remodeling-dependant