Universal Central Extensions of Gauge Algebras and Groups

We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed in [NW09], is universal. In doing so, we prove universality of the corresponding central extension of Lie algebras in a slightly more general setting.Comment: 9 pages, LaTeX. Changes w.r.t. version 2: minor changes (final version). To appear in J. Reine Angew. Mat

Development of the trade project and its role in Russian-french relations in the early 1680s

Introduction. The article considers the problems of Russian-French negotiations on the organization of trade between Russia and France in the first half of the 1680s.Materials and methods. The uniqueness of the study is facilitated by the use of materials from both Russian (Russian State Archive of Ancient Documents) and French archives (Archives du ministère des affaires étrangères), which have not previously been widely used in research. Thanks to the comprehensive use of documents from both sides, the study clarifies the details of the events that took place in the embassies and the specifics of their perception by the Russian and French courtiers. The analysis of the negotiations, their preparation and their procurement is conducted in the context of the methodology of new diplomatic history in order to establish the role of the trade question in the development of diplomatic relations between Russia and France.Results. The results of the study show the essential role of the Russian-French trade project in establishing direct connections between Russia and France, independent of changes in both countries policies towards the Polish-Lithuanian Commonwealth and Sweden. In the context of Russian court politics of the early 1680s, it is shown that both supporters of confrontation with Sweden and their adversaries, focusing on Russian participation in the anti-Ottoman coalition, were interested in rapprochement with France. At the same time, the preparation of the trade project led to analytical work in both countries that broadened their perceptions of each other, intensified contacts between representatives of both states, and led to the emergence of conjugate foreign policy projects.Conclusion. The work supplements the established in historiography conceptions of the organization of Russian diplomatic missions to France, the information about the role of the management of the Ambassador's office in this process, as well as the envoys and interpreters sent to France and their own perceptions of their place in this process

Deformation theory of objects in homotopy and derived categories III: abelian categories

This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consider examples from (noncommutative) algebraic geometry. In particular, we study noncommutative Grassmanians that are true noncommutative moduli spaces of structure sheaves of projective subspaces in projective spaces.Comment: Alexander Efimov is a new co-author of this paper. Besides some minor changes, a new part (part 3) about noncommutative Grassmanians was adde

Two-parametric deformation Up,q[gl(2/1)]U_{p,q}[gl(2/1)] and its induced representations

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical) finite-dimensional representations of this quantum superalgebra. In spite of some specific features, the present approach is similar to a previously developed method [1] which, as shown here, is applicable not only to the one-parametric quantum deformations but also to the multi-parametric ones.Comment: Latex, 13 pages, no figur

Russia on the French Roads to China in the second half of the XVII Century

The article examines the main attempts of French expansion into China, through the land route through Russia. To analyze the process, the author identifies areas associated with the diplomatic, cultural, religious and economic expansion of the kingdom of Louis XIV and the French nation (in its current meaning for the 17th century). Conclusions are drawn about the peculiarities of the geographical ideas about Russia in France, the process of perception of this knowledge through the space of the historical experience of the French, as well as the importance of the overland route to China for France in the 17th century are analyzed.В статье рассматриваются основные попытки французской экспансии в Китай посредством сухопутного пути через Россию. Для анализа процесса автором выделяются направления, связанные с дипломатической, культурно-религиозной и экономической экспансией королевства Людовика XIV и французской нации (в актуальном для XVII в., значении). Сделаны выводы об особенностях географических представлений о России во Франции, проанализирован процесс восприятия этих знаний через пространство исторического опыта французов, а также значение сухопутного пути в Китай для Франции XVII в

Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

Borcherds symmetries in M-theory

It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over the Grassmann algebra of differential forms on spacetime that have been shown to preserve the self-duality equation obeyed by all bosonic form-fields of the theory. We show here that the corresponding duality superalgebras are nothing but Borcherds superalgebras truncated by the above choice of Grassmann coefficients. The full Borcherds' root lattices are the second integral cohomology of the del Pezzo surfaces. Our choice of simple roots uses the anti-canonical form and its known orthogonal complement. Another result is the determination of del Pezzo surfaces associated to other string and field theory models. Dimensional reduction on $T^k$ corresponds to blow-up of $k$ points in general position with respect to each other. All theories of the Magic triangle that reduce to the $E_n$ sigma model in three dimensions correspond to singular del Pezzo surfaces with $A_{8-n}$ (normal) singularity at a point. The case of type I and heterotic theories if one drops their gauge sector corresponds to non-normal (singular along a curve) del Pezzo's. We comment on previous encounters with Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real fermionic simple roots when they would naively aris

A representation formula for maps on supermanifolds

In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation formula for all morphisms from the algebra of functions on an ordinary manifolds to the superalgebra of functions on an open subset of R^{p|q}. We then derive two consequences of this result. The first one is that we can integrate the data associated with a morphism in order to get a (non unique) map defined on an ordinary space (and uniqueness can achieved by restriction to a scheme). The second one is a simple and intuitive recipe to compute pull-back images of a function on a manifold by a map defined on a superspace.Comment: 23 page

Deformed Minkowski spaces: clasification and properties

Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz groups, which reproduces a previous classification by Woronowicz and Zakrzewski. As a consequence of the unified analysis presented, we give the commutation properties, the deformed (and central) length element and the metric tensor for the different spacetime algebras.Comment: Some comments/misprints have been added/corrected, to appear in Journal of Physics A (1996

Investigating the Contribution of Peri-domestic Transmission to Risk of Zoonotic Malaria Infection in Humans.

BACKGROUND: In recent years, the primate malaria Plasmodium knowlesi has emerged in human populations throughout South East Asia, with the largest hotspot being in Sabah, Malaysian Borneo. Control efforts are hindered by limited knowledge of where and when people get exposed to mosquito vectors. It is assumed that exposure occurs primarily when people are working in forest areas, but the role of other potential exposure routes (including domestic or peri-domestic transmission) has not been thoroughly investigated. METHODOLOGY/PRINCIPAL FINDINGS: We integrated entomological surveillance within a comprehensive case-control study occurring within a large hotspot of transmission in Sabah, Malaysia. Mosquitoes were collected at 28 pairs households composed of one where an occupant had a confirmed P. knowlesi infection within the preceding 3 weeks ("case") and an associated "control" where no infection was reported. Human landing catches were conducted to measure the number and diversity of mosquitoes host seeking inside houses and in the surrounding peri-domestic (outdoors but around the household) areas. The predominant malaria vector species was Anopheles balabacensis, most of which were caught outdoors in the early evening (6pm - 9pm). It was significantly more abundant in the peri-domestic area than inside houses (5.5-fold), and also higher at case than control households (0.28±0.194 vs 0.17±0.127, p<0.001). Ten out of 641 An. balabacensis tested were positive for simian malaria parasites, but none for P. knowlesi. CONCLUSIONS/SIGNIFICANCE: This study shows there is a possibility that humans can be exposed to P. knowlesi infection around their homes. The vector is highly exophagic and few were caught indoors indicating interventions using bednets inside households may have relatively little impact