Geometrical foundations of fractional supersymmetry

A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Berezin integral and fractional superspace measure arise as a natural part of our formalism. When $q$ is a root of unity the algebra is found to have a non-trivial Hopf structure, extending that associated with the anyonic line. One-dimensional ordinary/fractional superspace is identified with the braided line when $q$ is a root of unity, so that one-dimensional ordinary/fractional supersymmetry can be viewed as invariance under translation along this line. In our construction of fractional supersymmetry the $q$-deformed bosons play a role exactly analogous to that of the fermions in the familiar supersymmetric case.Comment: 42 pages, LaTeX. To appear in Int. J. Mod. Phys.

Braided structure of fractional Z3Z_3-supersymmetry

It is shown that fractional $Z_3$-superspace is isomorphic to the $q\to\exp(2\pi i/3)$ limit of the braided line. $Z_3$-supersymmetry is identified as translational invariance along this line. The fractional translation generator and its associated covariant derivative emerge as the $q\to\exp(2\pi i/3)$ limits of the left and right derivatives from the calculus on the braided lineComment: 8 pages, LaTeX, submitted to Proceedings of the 5th Colloquium `Quantum groups and integrable systems', Prague, June 1996 (to appear in Czech. J. Phys.

On the bicrossproduct structures for the Uλ(isoω2...ωN(N)){\cal U}_\lambda(iso_{\omega_2... \omega_N}(N)) family of algebras

It is shown that the family of deformed algebras ${\cal U}_\lambda(iso_{\omega_2... \omega_N}(N))$ has a different bicrossproduct structure for each $\omega_a=0$ in analogy to the undeformed case.Comment: Latex2e file. 14 page

Relativistic and Newtonian kappa spacetimes

The deformations of the Galilei algebra and their associated noncommutative Newtonian spacetimes are investigated. This is done by analyzing the possible nonrelativistic limits of an eleven generator (pseudo)extended \kap-Poincar\'e algebra $\tilde{\cal P}_\kappa$ and their implications for the existence of a first order differential calculus. The additional one-form needed to achieve a consistent calculus on \kap-Minkowski space is shown to be related to the additional central generator entering in the $\tilde{\cal P}_\kappa$ Hopf algebra. In the process, deformations of the extended Galilei and Galilei algebras are introduced which have, respectively, a cocycle and a bicrossproduct structure.Comment: Slightly shortened version with small changes to adapt the paper to JMP styl

Central extensions of the families of quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.Comment: 23 pages. Latex2e fil

Generalized Jacobi structures

Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a particular case, the recently introduced generalized Poisson structures. The linear case on simple group manifolds is also studied and non-trivial examples (different from those coming from generalized Poisson structures) of this new construction are found by using the cohomology ring of the given group.Comment: Latex2e file. 11 pages. To appear in J. Phys.

Representations of Quantum Bicrossproduct Algebras

We present a method to construct induced representations of quantum algebras having the structure of bicrossproduct. We apply this procedure to some quantum kinematical algebras in (1+1)--dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum kappa Galilei algebra.Comment: LaTeX 2e, 35 page

Revista de Vertebrados de la Estación Biológica de Doñana

Datos sobre la fauna de anfibios del Bajo GuadalquivirDiet of the Black Vulture (Aegypius monachus) in the Iberian PeninsulaBiología de reproducción de una pareja de Hieraetus fasciatus en España central.Sobre la migraclon de la focha común (Fulica atra) en el Mediterráneo Occidental en base a la información de la Estación Biológica de laTour du Valat (Camargue, Francia)Problemática y medidas de conservación de la Foca fraile (Monachus monachus, Hermann 1779) en el Sahara OccidentaNuevas citas de sifonápteros parásitos de mamíferos en España.Contribución al estudio de Lacerta monticola en la Sierra de Gredos (Avila. España)A melanistic Spanish smooth snake (Coranella a. austriaca)Nueva localidad para Vipera b. berus en el. Norte de EspañaSegunda cita en España de Porphyrula alleni (Thomson, 1842)Peer reviewe

Aerial mapping and multi-sensors approaches from remote sensing applied to the roman archaeological heritage

This report details the preliminary results of the research focused on Roman archaeological heritage in the Middle Ebro Valley (Spain). The principal objective of this project was to obtain several different readings by means of a UAV equipped with different sensors. Firstly, it has been possible to obtain accurate maps, 3D models and digital elevation models of the site. Secondly, it has been possible to investigate and define archaeological remains still underground, via a new methodology which utilises visible and near-infrared wavelengths