SUPERSYMMETRIC CONSTRUCTION OF W-ALGEBRAS FROM SUPER TODA AND WZNW THEORIES

A systematic construction of super W algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy momentum tensor, is discussed in general terms for all super Lie algebras whose simple roots are fermionic. A detailed discussion employing the Dirac bracket structure and an explicit construction of W algebras for the cases of OSP(1, 2), OSP(2, 2), OSP(3, 2) and D(2, 1\ alpha) are given. The N = 1 and N = 2 superconformal algebras are discussed in the pertinent cases.

Symplectic bosons, Fermi fields and super Jordan algebras

A construction relating the structures of super Lie and super Jordan algebras is proposed. This may clarify the role played by field theoretical realizations of super Jordan algebras in constructing representations of super Kač-Moody algebras. The case of OSP(m, n) and super Clifford algebras involving independent Fermi fields and symplectic bosons is discussed in detail.

Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas

Pós-graduação em Física - IFT

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

On delta-derivations of n-ary algebras

We give a description of delta-derivations of (n + 1)-dimensional n-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial delta-derivations of Filippov algebras and show that there are no non-trivial delta-derivations of the simple ternary Mal'tsev algebra M-8.

Radiosonde profiles and meteorological observations during Atlantic Expedition M2 in 1965 (IQSY) of RV "Meteor"

A radiosonde is described for measuring the upward and downward fluxes of visible light in the atmosphere. Photoresistors are used as sensors, the optical center of the spectral range beeing at 0.55 µ. The results of these flux-measurements obtained during the Atlantic Expedition 1965 with the research vessel "Meteor" are presented. The datas have been divided into three groups according to the amount of cloudiness. In group a) (small cloudiness) the extinction coefficient of the prevailing linear radiation is derived as a function of the height. Characteristics of airmasses of maritime or continental origin are shown. In group b) (cloud covered sky) microphysical quantities are determined from the radiative lapse rate in the clouds. The average radius of droplets is found to lie between 5.5 µm and 14.4 µm. The albedo of cloud surfaces varies between 25% and 54%, the transmission values are between 58% and 73%. One ascent through a Cirrus cloud of considerable vertical thickness is treated seperately. The observed distribution of extinction is compared with theoretical values in water clouds leading to the same order of magnitude. The relation between the albedo of the surface of the sea and the amount of cloudiness is discussed.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Nonabelian holomorphic Lie algebroid extensions

International audience

Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.

DJKM ALGEBRAS I: THEIR UNIVERSAL CENTRAL EXTENSION

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, g circle times C[t, t(-1), u vertical bar u(2) = (t(2) - b(2))(t(2) - c(2))], appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of integrable systems arising from the Landau-Lifshitz differential equation.

NMR structure of C-terminally tagged gramicidin channels

A biotin group was covalently attached to the C terminus of gramicidin A (gA) through a linker arm comprising a glycine residue with either one (gAXB) or two caproyl groups (gAXXB). High-resolution two-dimensional NMR spectroscopy was used to determine the structure of these modified gA analogues and [Lys(16)]gramicidin A (gA-Lys) in sodium dodecyl-d(25) sulphate micelles. Gated gA ion channels based on linking a receptor group to these gA analogues have been used recently as a component in a sensing device. The conformations of the gA backbones and amino acid side chains of lysinated gA and biotinylated gA in detergent micelles were found to be almost identical to that of native gA, i.e. that of an N-terminal to N-terminal (head to head) dimer formed by two right-handed, single-stranded beta(6.3) helices. The biotin tail of the gAXB and gAXXB and the lysine extremity of gA-Lys appeared to lie outside the micelle. Thus it appears that the covalent attachment of functional groups to the C terminus of gA does not disrupt the peptide's helical configuration. Further, single channel measurements of all three gA analogues showed that functioning ion channels were preserved within a membrane environment. (C) 1999 Elsevier Science B.V. All rights reserved.

Habitat use, diet and body size of Heard Island weevils

Habitat use, diet and body-size variation are examined in weevils from Heard Island. with specific attention being given to the Ectemnorhinus viridis species complex. E. viridis shows marked altitudinal variation in body size and vestiture, but there are no consistent associations between body size and diet. nor are there consistent among-individual differences in conventional taxonomic characters. Thus, the status of E. viridis as a single, variable species is maintained. This species occurs from sea level to 600 rn and it feeds on vascular plants and bryophytes. Canonopsis sericeus also feeds on bryophytes and vascular plants and occurs over a narrower altitudinal range. Palirhoeus eatoni is restricted to the surpralittoral zone where it feeds on marine algae and lichens. Bothrometopus brei,is and B. gracilipes both feed on cryptogams, with the former species occurring from sea level to 450 m. and the latter from 50 to 550 m above sea level. In all species, males are smaller than females and there is a size cline such that populations from higher elevations are smaller than those at lower altitudes. This cline is the reverse of that found on the Prince Edward Islands which, unlike Heard Island, lie to the north of the Antarctic Polar Frontal Zone. This difference in body-size clines between weevils on the two island groups is ascribed to the shorter growing season on the colder Heard Island. The information presented here supports previous ideas regarding the evolution of the Ectemnorhinus-group of weevils on the South Indian Ocean Province Islands, although it suggests that subsequent tests of these hypotheses would profit from the inclusion of molecular systematic work.

Mosaic maternal ancestry in the Great Lakes region of East Africa

The Great Lakes lie within a region of East Africa with very high human genetic diversity, home of many ethno-linguistic groups usually assumed to be the product of a small number of major dispersals. However, our knowledge of these dispersals relies primarily on the inferences of historical, linguistics and oral traditions, with attempts to match up the archaeological evidence where possible. This is an obvious area to which archaeogenetics can contribute, yet Uganda, at the heart of these developments, has not been studied for mitochondrial DNA (mtDNA) variation. Here, we compare mtDNA lineages at this putative genetic crossroads across 409 representatives of the major language groups: Bantu speakers and Eastern and Western Nilotic speakers. We show that Uganda harbours one of the highest mtDNA diversities within and between linguistic groups, with the various groups significantly differentiated from each other. Despite an inferred linguistic origin in South Sudan, the data from the two Nilotic-speaking groups point to a much more complex history, involving not only possible dispersals from Sudan and the Horn but also large-scale assimilation of autochthonous lineages within East Africa and even Uganda itself. The Eastern Nilotic group also carries signals characteristic of West-Central Africa, primarily due to Bantu influence, whereas a much stronger signal in the Western Nilotic group suggests direct West-Central African ancestry. Bantu speakers share lineages with both Nilotic groups, and also harbour East African lineages not found in Western Nilotic speakers, likely due to assimilating indigenous populations since arriving in the region ~3000 years ago.

NanoImpactNet - building a multi-stakeholder dialogue on the health and environmental impact of nanomaterials

NanoImpactNet (NIN) is a multidisciplinary European Commission funded network on the environmental, health and safety (EHS) impact of nanomaterials. The 24 founding scientific institutes are leading European research groups active in the fields of nanosafety, nanorisk assessment and nanotoxicology. This 4-year project is the new focal point for information exchange within the research community. Contact with other stakeholders is vital and their needs are being surveyed. NIN is communicating with 100s of stakeholders: businesses; internet platforms; industry associations; regulators; policy makers; national ministries; international agencies; standard-setting bodies and NGOs concerned by labour rights, EHS or animal welfare. To improve this communication, internet research, a questionnaire distributed via partners and targeted phone calls were used to identify stakeholders' interests and needs. Knowledge gaps and the necessity for further data mentioned by representatives of all stakeholder groups in the targeted phone calls concerned: • the potential toxic and safety hazards of nanomaterials throughout their lifecycles; • the fate and persistence of nanoparticles in humans, animals and the environment; • the associated risks of nanoparticle exposure; • greater participation in: the preparation of nomenclature, standards, methodologies, protocols and benchmarks; • the development of best practice guidelines; • voluntary schemes on responsibility; • databases of materials, research topics and themes, but also of expertise. These findings suggested that stakeholders and NIN researchers share very similar knowledge needs, and that open communication and free movement of knowledge will benefit both researchers and industry. Subsequently a workshop was organised by NIN focused on building a sustainable multi-stakeholder dialogue. Specific questions were asked to different stakeholder groups to encourage discussions and open communication. 1. What information do stakeholders need from researchers and why? The discussions about this question confirmed the needs identified in the targeted phone calls. 2. How to communicate information? While it was agreed that reporting should be enhanced, commercial confidentiality and economic competition were identified as major obstacles. It was recognised that expertise was needed in the areas of commercial law and economics for a wellinformed treatment of this communication issue. 3. Can engineered nanomaterials be used safely? The idea that nanomaterials are probably safe because some of them have been produced 'for a long time', was questioned, since many materials in common use have been proved to be unsafe. The question of safety is also about whether the public has confidence. New legislation like REACH could help with this issue. Hazards do not materialise if exposure can be avoided or at least significantly reduced. Thus, there is a need for information on what can be regarded as acceptable levels of exposure. Finally, it was noted that there is no such thing as a perfectly safe material but only boundaries. At this moment we do not know where these boundaries lie. The matter of labelling of products containing nanomaterials was raised, as in the public mind safety and labelling are connected. This may need to be addressed since the issue of nanomaterials in food, drink and food packaging may be the first safety issue to attract public and media attention, and this may have an impact on 'nanotechnology as a whole. 4. Do we need more or other regulation? Any decision making process should accommodate the changing level of uncertainty. To address the uncertainties, adaptations of frameworks such as REACH may be indicated for nanomaterials. Regulation is often needed even if voluntary measures are welcome because it mitigates the effects of competition between industries. Data cannot be collected on voluntary bases for example. NIN will continue with an active stakeholder dialogue to further build on interdisciplinary relationships towards a healthy future with nanotechnology.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.