Symbolic approach and induction in the Heisenberg group

We associate a homomorphism in the Heisenberg group to each hyperbolic unimodular automorphism of the free group on two generators. We show that the first return-time of some flows in "good" sections, are conjugate to niltranslations, which have the property of being self-induced.Comment: 18 page

Ternary algebras and groups

We construct explicitly groups associated to specific ternary algebras which extend the Lie (super)algebras (called Lie algebras of order three). It turns out that the natural variables which appear in this construction are variables which generate the three-exterior algebra. An explicit matrix representation of a group associated to a peculiar Lie algebra of order three is constructed considering matrices with entry which belong to the three exterior algebra.Comment: 11 pages contribution to the 5th International Symposium on Quantum Theory and Symmetries (QTS5

On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased; author's version of the published pape

Quasi-classical Lie algebras and their contractions

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras.Comment: 17 pages, 2 Table

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

On Deformations of n-Lie algebras

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other author

Helping farmers adapt to climate and cropping system change through increased access to sorghum genetic resources adapted to prevalent sorghum cropping systems in Burkina Faso

Sorghum (Sorghum bicolor (L.) Moench) is a major staple crop of Burkina Faso where farmers continue to cultivate photoperiod-sensitive guinea landraces as part of the strategy to minimize risk and ensure yield stability. In the Boucle du Mouhoun region, however, sorghum farmers appear to have insufficient varietal choice due to cropping systems having shifted towards more intensive cultivation of cotton and maize, and rainfall patterns having decreased over the past decade. In search for new varietal options that can respond to this changing context, researchers decided to give farmers access to ex-situ national collections along with the opportunity to evaluate recent improved varieties. From 2002 to 2007, researchers and farmers worked closely together to implement on-farm testing, including varietal selection trials, crop management and multi-locational trials. Farmers’ choices tend to differ among groups, villages and years, with the exception of four particular landraces: two originating from a collection carried out in the Mouhoun region more than 30 years previous to this research, and two other landraces that came from the dissimilar agro-ecological zones of Burkina Faso. These four were the most commonly selected landraces out of 36 cultivars that covered both improved and landrace varieties. Farmers’ selection criteria were focused on adaptation to agro-climatic conditions as well as specific grain qualities for processing and consumption. The potential usefulness of each variety was verified via multi-locational trials. The paper also shows that wide dissemination of experimental seed, not just across the Mouhoun region but also at a national scale, was largely achieved through collaboration with a strong farmer organisation in conjunction with farmer training programs focused on the on-farm seed production and the commercialisation of this seed

Some Results on Cubic and Higher Order Extensions of the Poincar\'e Algebra

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra. We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the Poincar\'e algebra or Supersymmetry. Some general features on the so-called Wess-Zumino model (the simplest field theory invariant under Supersymmetry) are then given. We further introduce an additional algebraic structure called Lie algebras of order F, which naturally comprise the concepts of ordinary Lie algebras and superalgebras. This structure enables us to define various non-trivial extensions of the Poincar\'e algebra. These extensions are studied more precisely in two different contexts. The first algebra we are considering is shown to be an (infinite dimensional) higher order extension of the Poincar\'e algebra in $(1+2)-$dimensions and turns out to induce a symmetry which connects relativistic anyons. The second extension we are studying is related to a specific finite dimensional Lie algebra of order three, which is a cubic extension of the Poincar\'e algebra in $D-$space-time dimensions. Invariant Lagrangians are constructed.Comment: Mini course given at the Workshop higher symmetries in physics, Madrid, Spain, November 6-8, 200

Structure and vibrational properties of single wall carbon nanotubes

We report on some Raman measurements of single wall carbon nanotubes (SWNT) prepared by laser ablation (LA) or electric arc discharge (EA). We correlate the Raman features with structural information and discuss the resonance behaviour of the Raman signal in terms of a distribution of tubes diameters and symmetries.Peer reviewe

Normosmic Congenital Hypogonadotropic Hypogonadism Due to TAC3/TACR3 Mutations: Characterization of Neuroendocrine Phenotypes and Novel Mutations

CONTEXT: TAC3/TACR3 mutations have been reported in normosmic congenital hypogonadotropic hypogonadism (nCHH) (OMIM #146110). In the absence of animal models, studies of human neuroendocrine phenotypes associated with neurokinin B and NK3R receptor dysfunction can help to decipher the pathophysiology of this signaling pathway. OBJECTIVE: To evaluate the prevalence of TAC3/TACR3 mutations, characterize novel TACR3 mutations and to analyze neuroendocrine profiles in nCHH caused by deleterious TAC3/TACR3 biallelic mutations. RESULTS: From a cohort of 352 CHH, we selected 173 nCHH patients and identified nine patients carrying TAC3 or TACR3 variants (5.2%). We describe here 7 of these TACR3 variants (1 frameshift and 2 nonsense deleterious mutations and 4 missense variants) found in 5 subjects. Modeling and functional studies of the latter demonstrated the deleterious consequence of one missense mutation (Tyr267Asn) probably caused by the misfolding of the mutated NK3R protein. We found a statistically significant (p<0.0001) higher mean FSH/LH ratio in 11 nCHH patients with TAC3/TACR3 biallelic mutations than in 47 nCHH patients with either biallelic mutations in KISS1R, GNRHR, or with no identified mutations and than in 50 Kallmann patients with mutations in KAL1, FGFR1 or PROK2/PROKR2. Three patients with TAC3/TACR3 biallelic mutations had an apulsatile LH profile but low-frequency alpha-subunit pulses. Pulsatile GnRH administration increased alpha-subunit pulsatile frequency and reduced the FSH/LH ratio. CONCLUSION: The gonadotropin axis dysfunction associated with nCHH due to TAC3/TACR3 mutations is related to a low GnRH pulsatile frequency leading to a low frequency of alpha-subunit pulses and to an elevated FSH/LH ratio. This ratio might be useful for pre-screening nCHH patients for TAC3/TACR3 mutations