Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation

Z_2-gradings of Clifford algebras and multivector structures

Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.Comment: 10 pages, LaTeX; v2 accepted for publication in J. Phys.

Inhibition of Membrane-Bound BAFF by the Anti-BAFF Antibody Belimumab.

B cell activating factor of the TNF family (BAFF, also known as BLyS), a cytokine that regulates homeostasis of peripheral B cells, is elevated in the circulation of patients with autoimmune diseases such as systemic lupus erythematosus (SLE). BAFF is synthetized as a membrane-bound protein that can be processed to a soluble form after cleavage at a furin consensus sequence, a site that in principle can be recognized by any of the several proteases of the pro-protein convertase family. Belimumab is a human antibody approved for the treatment of SLE, often cited as specific for the soluble form of BAFF. Here we show in different experimental systems, including in a monocytic cell line (U937) that naturally expresses BAFF, that belimumab binds to membrane-bound BAFF with similar EC50 as the positive control atacicept, which is a decoy receptor for both BAFF and the related cytokine APRIL (a proliferation inducing ligand). In U937 cells, binding of both reagents was only detectable in furin-deficient U937 cells, showing that furin is the main BAFF processing protease in these cells. In CHO cells expressing membrane-bound BAFF lacking the stalk region, belimumab inhibited the activity of membrane-bound BAFF less efficiently than atacicept, while in furin-deficient U937 cells, belimumab inhibited membrane-bound BAFF and residual soluble BAFF as efficiently as atacicept. These reagents did not activate complement or antibody-dependent cell cytotoxicity upon binding to membrane-bound BAFF in vitro. In conclusion, our data show that belimumab can inhibit membrane-bound BAFF, and that BAFF in U937 cells is processed by furin

Spin, Statistics, and Reflections, II. Lorentz Invariance

The analysis of the relation between modular P$_1$CT-symmetry -- a consequence of the Unruh effect -- and Pauli's spin-statistics relation is continued. The result in the predecessor to this article is extended to the Lorentz symmetric situation. A model \G_L of the universal covering \widetilde{L_+^\uparrow}\cong SL(2,\complex) of the restricted Lorentz group $L_+^\uparrow$ is modelled as a reflection group at the classical level. Based on this picture, a representation of \G_L is constructed from pairs of modular P$_1$CT-conjugations, and this representation can easily be verified to satisfy the spin-statistics relation

Reversal of the hip fracture secular trend is related to a decrease in the incidence in institution-dwelling elderly women

Summary: In this prospective 10-year study in elderly aged 60years and over, there was a 1.3% per year reduction in the standardized incidence of hip fracture in women but not in men. This decrease was mainly due to changes in the standardized incidence of hip fracture in institution-dwelling women. Introduction: A decrease in age-adjusted hip fracture incidence has been recently demonstrated in some countries. Since a large proportion of hip fractures occur in nursing homes, we analyzed whether this decreasing trend would be more detectable in institution-dwelling elderly compared with community-dwelling elderly. Methods: All hip fracture patients aged 60years and over were identified in a well-defined area. Incidence of hip fracture, age- and sex-adjusted to the 2000 Geneva population, was computed in community- and institution-dwelling elderly. Results: From 1991 to 2000, 1,624 (41%) hip fractures were recorded in institutionalized-dwelling elderly and 2,327 (59%) in community-dwelling elderly. The standardized fracture incidence decreased by 1.3% per year in women (p = 0.039), but remained unchanged in men (+0.5%; p = 0.686). Among institution-dwelling women, hip fracture incidence fell by 1.9% per year (p = 0.044), whereas it remained stable among community-dwelling women (+0.0%, p = 0.978). In men, no significant change in hip fracture incidence occurred among institution- or community-dwelling elderly. Conclusions: The decrease in the standardized hip fracture incidence in institution-dwelling women is responsible for the reversal in secular trend. Future research should include stratification according to the residential status to better identify the causes responsible for the trend in hip fracture incidenc

Cosmology, cohomology, and compactification

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.Comment: 6 pages, LaTe

A planar extrapolation of the correlation problem that permits pairing

It was observed previously that an SU(N) extension of the Hubbard model is dominated, at large N, by planar diagrams in the sense of 't Hooft, but the possibility of superconducting pairing got lost in this extrapolation. To allow for this possibility, we replace SU(N) by U(N,q), the unitary group in a vector space of quaternions. At the level of the free energy, the difference between the SU(N)and U(N,q) extrapolations appears only to first nonleading order in N.Comment: 8 pages, 2 figure

Singular riemannian foliations with sections, transnormal maps and basic forms

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally and whose dimension is the codimension of the regular leaves of F. We prove that the algebra of basic forms of M relative to F is isomorphic to the algebra of those differential forms on a section that are invariant under the generalized Weyl pseudogroup of this section. This extends a result of Michor for polar actions. It follows from this result that the algebra of basic function is finitely generated if the sections are compact. We also prove that the leaves of F coincide with the level sets of a transnormal map (generalization of isoparametric map) if M is simply connected, the sections are flat and the leaves of F are compact. This result extends previous results due to Carter and West, Terng, and Heintze, Liu and Olmos.Comment: Preprint IME-USP; The final publication is available at springerlink.com http://www.springerlink.com/content/q48682633730t831

Paraboson quotients. A braided look at Green ansatz and a generalization

Bosons and Parabosons are described as associative superalgebras, with an infinite number of odd generators. Bosons are shown to be a quotient superalgebra of Parabosons, establishing thus an even algebra epimorphism which is an immediate link between their simple modules. Parabosons are shown to be a super-Hopf algebra. The super-Hopf algebraic structure of Parabosons, combined with the projection epimorphism previously stated, provides us with a braided interpretation of the Green's ansatz device and of the parabosonic Fock-like representations. This braided interpretation combined with an old problem leads to the construction of a straightforward generalization of Green's ansatz.Comment: 33 pages, Corrected a few misprints and typos of the journal versio