On the center of 3-dimensional and 4-dimensional Sklyanin algebras

In this article, a new proof is given of the description of the center of quadratic Sklyanin algebras of global dimension three and four and the center of cubic Sklyanin algebras of global dimension three. The representation theory of the Heisenberg groups $H_2$, $H_3$ and $H_4$ will play an important role. In addition a new proof is given of Van den Bergh's result regarding noncommutative quadrics.Comment: 16 page

Point modules of quantum projective spaces

In this note we give an explicit description of the irreducible components of the reduced point varieties of quantum polynomial algebras.Comment: 4 pages, a short not

The point variety of quantum polynomial rings

We show that the reduced point variety of a quantum polynomial algebra is the union of specific linear subspaces in $\mathbb{P}^n$, we describe its irreducible components and give a combinatorial description of the possible configurations in small dimensions.Comment: 10 pages, an extended version of arxiv.org/abs/1506.0651

L’oeuvre de Guillaume IX d’Aquitaine et son processus de traduction : un retour aux sources. Reconstruction annotée de la Canso V

Joseph (Jef) Barthels (1943-1999) nous a laissé la traduction, inédite à ce jour, en vers français et néerlandais de l’oeuvre complète de Guillaume IX d’Aquitaine. Publiée à titre posthume, cette contribution implique l’analyse du processus de traduction et le retour aux sources orales et écrites. Nous tentons de tester l’intertextualité entre les histoires du Roman de Renart et les chansons occitanes de Guillaume, qui fonde la vision et la méthodologie du traducteur.Joseph (Jef) Barthels (1943-1999) left us the hitherto unpublished translation in French and Dutch verse of William IX of Aquitaine’s entire works. The publication of this significant contribution to modern scholarship implies an analysis of the translation process and a return to the oral and written sources. An attempt will be made to test the validity of intertextual relations between the stories in Le Roman de Renart and William’s Occitan songs as these lie at the heart of the translator’s vision and methodology

Elementos no atomismo, segundo Aristóteles

In this paper, I discuss the use made by Aristotle of the term “element” when dealing with the atomist theory of Leucippus and Democritus. My goal is to verify which aspects of the atomist theory play the role of elements according to the definitions of Aristotle, who seems to have certain expectations regarding what can be designated as elements in the strict sense. One of them is the possibility of reciprocal transformation, the so-called “generation of elements”, which is the chemical aspect at the level of the simple bodies that makes change possible at the level of sense-perceived bodies. Furthermore, I evaluate whether it is possible to find and whether it is adequate to speak of the presence of the four elements – fire, air, water and earth – in the atomist doctrine

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