K1 of Chevalley groups are nilpotent

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Polybius’ ‘previous landslide’: Proof that Hannibal’s invasion route crossed the col de la traversette

Both Polybius and Livy described a landslide/landslip that blocked the Punic Army’s exfiltration from a high col on the water divide in the Western Alps. The landslide, more aptly termed rockfall, has been a source of contention amongst classicists for centuries despite the fact that only two cols—Clapier and Traversette—exhibit rockfall debris on the lee side of the Alps. While the Clapier rockfall is too small and too young to have provided blockage, the Traversette debris is nearly as Polybius described it when he retraced the invasion route some 60 years after the event. His ‘two-tier’ description of the deposit, a doublet of younger and older rock rubble, including measurements of width and volume are close to modern measurements and prove that he knew, in advance, the route Hannibal had followed. It would take a practiced eye to correctly identify the stratigraphic complexity inherent in the Traversette Rockfall. Here we present weathering ratios, soil stratigraphic, mineral, chemical and microbiological evidence in support of Polybius’ observations as a considerable background database for future geoarchaeological exploration.

Narrative Bifurcation, Cloud Computing Interfaces and Hitchcok

From a narratological perspective, this paper aims to address the theoretical issues concerning the functioning of the so called «narrative bifurcation» in data presentation and information retrieval. Its use in cyberspace calls for a reassessment as a storytelling device. Films have shown its fundamental role for the creation of suspense. Interactive fiction and games have unveiled the possibility of plots with multiple choices, giving continuity to cinema split-screen experiences. Using practical examples, this paper will show how this storytelling tool returns to its primitive form and ends up by conditioning cloud computing interface design.