The family of quaternionic quasi-unitary Lie algebras and their central extensions

The family of quaternionic quasi-unitary (or quaternionic unitary Cayley--Klein algebras) is described in a unified setting. This family includes the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well as many non-semisimple real Lie algebras which can be obtained from these simple algebras by particular contractions. The algebras in this family are realized here in relation with the groups of isometries of quaternionic hermitian spaces of constant holomorphic curvature. This common framework allows to perform the study of many properties for all these Lie algebras simultaneously. In this paper the central extensions for all quasi-simple Lie algebras of the quaternionic unitary Cayley--Klein family are completely determined in arbitrary dimension. It is shown that the second cohomology group is trivial for any Lie algebra of this family no matter of its dimension.Comment: 17 pages, LaTe

Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature

An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two different subsets of N integrals in involution (including the Hamiltonian) can always be explicitly identified. As particular cases, we recover in a straightforward way most of the superintegrability properties of the Smorodinsky-Winternitz and generalized Kepler-Coulomb systems on spaces of constant curvature and we introduce as well new classes of (quasi-maximally) superintegrable potentials on these spaces. Results here presented are a consequence of the sl(2) Poisson coalgebra symmetry of all the Hamiltonians, together with an appropriate use of the phase spaces associated to Poincare and Beltrami coordinates.Comment: 12 page

Integrable potentials on spaces with curvature from quantum groups

A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson coalgebra. All these spaces have a non-constant curvature that depends on the deformation parameter z. As particular cases, the analogues of the harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed. Another deformed Hamiltonian is also shown to provide superintegrable systems on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant curvature that exactly coincides with z. According to each specific space, the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers. The non-deformed limit z=0 of all these Hamiltonians can then be regarded as the zero-curvature limit (contraction) which leads to the corresponding (super)integrable systems on the flat Euclidean and Minkowskian spaces.Comment: 19 pages, 1 figure. Two references adde

Herschel-ATLAS: Evolution of the 250 µm luminosity function out to z = 0.5

5 páginas, 4 figuras.-- Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.-- et al.We have determined the luminosity function of 250 μm-selected galaxies detected in the ~14 deg2 science demonstration region of the Herschel-ATLAS project out to a redshift of z = 0.5. Our findings very clearly show that the luminosity function evolves steadily out to this redshift. By selecting a sub-group of sources within a fixed luminosity interval where incompleteness effects are minimal, we have measured a smooth increase in the comoving 250 μm luminosity density out to z = 0.2 where it is 3.6+1.4-0.9 times higher than the local value.S.D. Acknowledges the UK STFC for support.Peer reviewe

New time-type and space-type non-standard quantum algebras and discrete symmetries

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed by using a graded contraction scheme; these are realized as deformations of conformal algebras of (1+1)-dimensional spacetimes. Time-type and space-type quantum algebras are considered according to the generator that remains primitive after deformation: either the time or the space translation, respectively. Furthermore by introducing differential-difference conformal realizations, these families of quantum algebras are shown to be the symmetry algebras of either a time or a space discretization of (1+1)-dimensional (wave and Laplace) equations on uniform lattices; the relationship with the known Lie symmetry approach to these discrete equations is established by means of twist maps.Comment: 17 pages, LaTe

Bicrossproduct structure of the null-plane quantum Poincare algebra

A nonlinear change of basis allows to show that the non-standard quantum deformation of the (3+1) Poincare algebra has a bicrossproduct structure. Quantum universal R-matrix, Pauli-Lubanski and mass operators are presented in the new basis.Comment: 7 pages, LaTe

Graded contractions of bilinear invariant forms of Lie algebras

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Killing form, toroidal contractions of $su(3)$, and we briefly discuss the limit to new WZW actions.Comment: 15 page

Induction of Paralysis and Visual System Injury in Mice by T Cells Specific for Neuromyelitis Optica Autoantigen Aquaporin-4.

While it is recognized that aquaporin-4 (AQP4)-specific T cells and antibodies participate in the pathogenesis of neuromyelitis optica (NMO), a human central nervous system (CNS) autoimmune demyelinating disease, creation of an AQP4-targeted model with both clinical and histologic manifestations of CNS autoimmunity has proven challenging. Immunization of wild-type (WT) mice with AQP4 peptides elicited T cell proliferation, although those T cells could not transfer disease to naïve recipient mice. Recently, two novel AQP4 T cell epitopes, peptide (p) 135-153 and p201-220, were identified when studying immune responses to AQP4 in AQP4-deficient (AQP4-/-) mice, suggesting T cell reactivity to these epitopes is normally controlled by thymic negative selection. AQP4-/- Th17 polarized T cells primed to either p135-153 or p201-220 induced paralysis in recipient WT mice, that was associated with predominantly leptomeningeal inflammation of the spinal cord and optic nerves. Inflammation surrounding optic nerves and involvement of the inner retinal layers (IRL) were manifested by changes in serial optical coherence tomography (OCT). Here, we illustrate the approaches used to create this new in vivo model of AQP4-targeted CNS autoimmunity (ATCA), which can now be employed to study mechanisms that permit development of pathogenic AQP4-specific T cells and how they may cooperate with B cells in NMO pathogenesis

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe