Y-algebroids and E7(7)×R+E_{7(7)} \times \mathbb{R}^+-generalised geometry

We define the notion of Y-algebroids, generalising the Lie, Courant, and exceptional algebroids that have been used to capture the local symmetry structure of type II string theory and M-theory compactifications to $D \geq 5$ dimensions. Instead of an invariant inner product, or its generalisation arising in exceptional algebroids, Y-algebroids are built around a specific type of tensor, denoted $Y$, that provides exactly the necessary properties to also describe compactifications to $D=4$ dimensions. We classify ``M-exact'' $E_7$-algebroids and show that this precisely matches the form of the generalised tangent space of $E_{7(7)} \times \mathbb{R}^+$-generalised geometry, with possible twists due to 1-, 4- and 7-form fluxes, corresponding physically to the derivative of the warp factor and the M-theory fluxes. We translate the notion of generalised Leibniz parallelisable spaces, relevant to consistent truncations, into this language, where they are mapped to so-called exceptional Manin pairs. We also show how to understand Poisson--Lie U-duality and exceptional complex structures using Y-algebroids.Comment: 19 page

Courant algebroids and string low energy effective actions

Cette thèse est consacrée à l'application des méthodes de la géométrie de Poisson dans le contexte de la théorie des cordes, notamment pour étudier la limite d'énergie basse et les dualités de cette dernière. Les résultats contenus dans la thèse sont les suivants: - Reformulation des notions de tenseur de Ricci et de courbure scalaire généralisées aux algébroïdes de Courant. - Dérivation de ces tenseurs de courbure à partir de la variation d'une action naturelle. - Preuve de la compatibilité de la T-dualité de Poisson-Lie avec les transformations infinitésimales du groupe de renormalisation à une boucle, dans la configuration générale. - Preuve de la compatibilité de la T-dualité de Poisson-Lie avec la partie bosonique des équations d'arrière-plan pour les 5 théories des supercordes. - Découverte des nouvelles classes de solutions d’équations de supergravité modifiées sur des espaces symétriques

Term-day magnetic observations from the Prague-Clementinum observatory on 1845-06-19

Data of term-day observations recorded at the Prague-Clementinum observatory in years 1840-1849 are presented. The data were obtained by digitising and processing the original old records published in the yearbooks of this historical observatory. The term-day observations had been agreed for joint measurements by the observatories organised in the Göttingen Magnetic Union (GMU). Data of 120 term-days from January 1840 to December 1849 are published. The observations started at 10 p.m. of Göttingen Mean Time and lasted 24 hours. The interval between observations was 5 minutes (in April, June and July 1842 exceptionally 6 minutes). All time data were transformed into UT, based on the longitude of the Göttingen observatory, which was 9.950°. The time shift is thus 39'48''. The date in the term-day file name indicates the second day which involves substantial part of the observations (22 out of 24 hours)