Diagonal automorphisms of the 22-adic ring C∗C^*-algebra

The $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$ naturally contains a copy of the Cuntz algebra $\mathcal{O}_2$ and, a fortiori, also of its diagonal subalgebra $\mathcal{D}_2$ with Cantor spectrum. This paper is aimed at studying the group ${\rm Aut}_{\mathcal{D}_2}(\mathcal{Q}_2)$ of the automorphisms of $\mathcal{Q}_2$ fixing $\mathcal{D}_2$ pointwise. It turns out that any such automorphism leaves $\mathcal{O}_2$ globally invariant. Furthermore, the subgroup ${\rm Aut}_{\mathcal{D}_2}(\mathcal{Q}_2)$ is shown to be maximal abelian in ${\rm Aut}(\mathcal{Q}_2)$. Saying exactly what the group is amounts to understanding when an automorphism of $\mathcal{O}_2$ that fixes $\mathcal{D}_2$ pointwise extends to $\mathcal{Q}_2$. A complete answer is given for all localized automorphisms: these will extend if and only if they are the composition of a localized inner automorphism with a gauge automorphism.Comment: Improved exposition and corrected some typos and inaccuracie

A look at the inner structure of the 2-adic ring C*-algebra and its automorphism groups

We undertake a systematic study of the so-called 2-adic ring C\u87-algebra Q2. This is the universal C\u87-algebra generated by a unitary U and an isometry S2 such that S2U = U2S2 and S2S\u87 2+US2S\u87 2U\u87 = 1. Notably, it contains a copy of the Cuntz algebra O2 = C\u87(S1;S2) through the injective homomorphism mapping S1 to US2. Among the main results, the relative commutant C\u87(S2)\u9c 9 Q2 is shown to be trivial. This in turn leads to a rigidity property enjoyed by the inclusion O2 ` Q2, namely the endomorphisms of Q2 that restrict to the identity on O2 are actually the identity on the whole Q2. Moreover, there is no conditional expectation from Q2 onto O2. As for the inner structure of Q2, the diagonal subalgebra D2 and C\u87(U) are both proved to be maximal abelian in Q2. The maximality of the latter allows a thorough investigation of several classes of endomorphisms and automorphisms of Q2. In particular, the semigroup of the endomorphisms xing U turns out to be a maximal abelian subgroup of Aut(Q2) topologically isomorphic with C(T;T). Finally, it is shown by an explicit construction that Out(Q2) is uncountable and non- abelian

The Homflypt polynomial and the oriented Thompson group

We show how to construct unitary representations of the oriented Thompson group $\vec{F}$ from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of $\vec{F}$.Comment: To appear in Quantum Topolog

Sando Marteu: il cantore di Lubumbashi

This article stems from a field research carried out in Lubumbashi in September and October 2018, as part of a national project on contemporary RDC, with a focus on the swahilophone creative expressions. It aims at outlining the poetics of the sing-songwriter Sando Marteau as it springs from his texts in Swahili, within the linguistic and cultural context of Lubumbashi

Poesia swahili in Katanga: multilinguismo e corporalità nei versi di Patrick Mudekereza

The world of Swahili contemporary poetry, as remarked by M. M. Mulokozi and T. S. Y. Sengo (1995: 22), is amazingly broad, given the progressive diffusion of the Swahili language in the course of the last two centuries, from the East African coast to the continental regions of Eastern and Central Africa. Accordingly, authors of Swahili poetic texts can also be found in the “periphery” of the Swahilophone area, such as the Democratic Republic of Congo, where this language has become the medium of modern songs and written poetry in many areas, although the latter is hardly visible in a context where creative writing is predominantly expressed in French.In the present contribution, after an introduction on Swahili poetry in the DRC and on the linguistic complexity of the Swahilophone environment of Katanga, and particularly of its main city, Lubumbashi, we will present some (so far unpublished) poems by Patrick Mudekereza, art curator and director of the cultural centre WAZA, together with a first analysis of his verses, whose poetics emerges from plurilingualism and corporality

An Hybrid FE/SEA Approach for Engine Cover Noise Assessment

In this paper a deep numerical analysis on an internal combustion engine’s cover is carried out. An Hybrid numerical model approach to evaluate the acoustic performance of engine's cover, has been used. The Hybrid model is composed of two numerical models: FE and SEA models. The model FE patterns the structural system, whilst model SEA patterns the acoustic environment. As main excitation an experimental data has been used for two considered engine conditions. The comparison in terms of sound pressure levels between the experimental and FEM/SEA analysis results shows a very good agreement, in the whole investigated frequency range. The obtained results encourage to use the numerical model for further investigations aimed at the improvement of its acoustic performances. The implemented numerical procedure can be applied successfully not only in automotive field but also in all problems where material acoustic performances, is due

Experimental and Numerical Validation of an Automotive Subsystem through the Employment of FEM/BEM Approaches

Abstract In this paper a deep numerical analysis on an internal combustion engine cover is carried out. A hybrid numerical model has been used to evaluate the acoustic performance of engine cover. The Hybrid model is composed of two numerical models: FE (Finite Element) and BEM (Boundary Element Method) models. The FE model patterns structural system, whilst BEM model patterns fluid environment. The main aim of the present work is to characterize, through the employment of numerical simulation, the acoustic performance of the engine cover by using the NR (Noise Reduction) parameter. The numerical frequency response analysis has been implemented using acoustic impedance experimental data, measured for four different thicknesses of sound proof material forming the cover system. The spectrum of acoustic impedance has been evaluated in near field with a sophisticated probe, pressure-velocity probe (p-v probe). The analysis of the obtained results have highlighted the weaknesses as regards sound attenuation of the cover system and possible further improvements of cover system acoustic performance

A Hitchhiker's Guide to Endomorphisms and Automorphisms of Cuntz Algebras

We present a broad selection of results on endomorphisms and automorphisms of the Cuntz algebras $mathcal{O}_n$ that have been obtained in the last decades. A wide variety of open problems is also included