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.

INTEGRABLE MODULES FOR AFFINE LIE SUPERALGEBRAS

Irreducible nonzero level modules with finite-dimensional weight spaces are discussed for nontwisted affine Lie superalgebras. A complete classification of such modules is obtained for superalgebras of type A(m, n)(boolean AND) and C(n)(boolean AND) using Mathieu's classification of cuspidal modules over simple Lie algebras. In other cases the classification problem is reduced to the classification of cuspidal modules over finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu and Penkov. Based on these results a. complete classification of irreducible integrable (in the sense of Kac and Wakimoto) modules is obtained by showing that any such module is of highest weight, in which case the problem was solved by Kac and Wakimoto.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Neuropharmacological effects in mice of Lychnophora species (Vernonieae, Asteraceae) and anticonvulsant activity of 4,5-di-O-[E]-caffeoylquinic acid isolated from the stem of L-rupestris and L-staavioides

Aiming at contributing with the search for neuroactive substances from natural sources, we report for the first time antinociceptive and anticonvulsant effects of some Lychnophora species. We verify the protective effects of polar extracts (600 mg/kg, intraperitoneally), and methanolic fractions of L. staavioides and L. rupestris (100 mg/kg, intraperitoneally) in pentylenetetrazole-induced seizures on mice. Previously, a screening was accomplished, evaluating the antinociceptive central activity (hot plate test), with different extracts of L. rupestris, L. staavioides and L. diamantinana. It was possible to select the possible extracts of Lychnophora with central nervous system activity. Some of the active extracts were submitted to fractionation and purification process and the methanolic fractions of L. rupestris (stem) and L. staavioides (stem), with anticonvulsant properties (100 mg/kg, intraperitoneally), yielded 4,5-di-O-[E]-caffeoylquinic acid. This substance was injected intraperitoneally in mice and showed anticonvulsant effect against pentylenetetrazole-induced seizures at doses of 25 and 50 mg/kg. It has often been shown that seizures induced by pentylenetetrazole are involved in inhibition and/or attenuation of GABAergic neurotransmission. However, other systems of the central nervous system such as adenosinergic and glutamatergic could be involved in the caffeoylquinic acid effects. Further studies should be conducted to verify that the target receptor could be participating in this anticonvulsant property. Although other investigations have reported a series of biological activities from Lychnophora species, this is the first report of central analgesic and anticonvulsant activity in species of this genus.

Copper(II) complexes of mono- and di-nucleating hexaamines

The potentially hexadentate polyamines N,N,N',N'-tetrakis(2-aminoethyl)ethane-1,2-diamine (L-1) and the octamethylated analogue N,N,N',N'-tetrakis(2-dimethylaminoethyl)ethane 1,2-diamine (L-2) have been complexed with copper(II) and the crystal structures of their complexes determined. A trigonal-bipyramidal co-ordination geometry for [Cu(HL1)][ClO4](3) was found where one aminoethyl arm is not co-ordinated. By contrast, a dinuclear structure of formula [(H2O)Cu(L-2)Cu(OH)](3+) was determined for the N-methylated analogue, where the hexaamine acts as a bridging ligand between the two square-pyramidal metal centres. Electronic and EPR spectroscopy are both consistent with these structures being maintained in solution.

Stage-specific proteophosphoglycan from Leishmania mexicana amastigotes - Structural characterization of novel mono-, di-, and triphosphorylated phosphodiester-linked oligosaccharides

Intracellular amastigotes of the protozoan parasite Leishmania mexicana secrete a macromolecular proteophosphoglycan (aPPG) into the phagolysosome of their host cell, the mammalian macrophage. The structures of aPPG glycans were analyzed by a combination of high pH anion exchange high pressure liquid chromatography, gas chromatography-mass spectrometry, enzymatic digestions, electrospray-mass spectrometry as well as H-1 and P-31 NMR spectroscopy. Some glycans are identical to oligosaccharides known from Leishmania mexicana promastigote lipophosphoglycan and secreted acid phosphatase, However, the majority of the aPPG glycans represent amastigote stage-specific and novel structures. These include neutral glycans ([Glc beta(1-3)](1-2)Gal beta 1-4Man, Gal beta 1-3Gal beta 1-4Man, Gal beta 1-3Glc beta 1-3Gal beta 1-4Man), several monophosphorylated glycans containing the conserved phosphodisaccharide backbone (R-3-[PO4-6-Gal]beta 1-4Man) but carrying stage-specific modifications (R = Gal beta 1-, [Glc beta 1-3](1-2)Glc beta 1-), and monophosphorylated aPPG tri- and tetrasaccharides that are uniquely phosphorylated on the terminal hexose (PO4-6-Glc beta 1-3Gal beta 1-4Man, PO4-6-Glc beta 1-3Glc beta 1-3Gal beta 1-4Man, PO4-6-Gal beta 1-3Glc beta 1-3Gal beta 1-4Man), In addition aPPG contains highly unusual di- and triphosphorylated glycans whose major species are PO4-6-Glc beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man, PO4-6-Gal beta 1-3Glc beta 1-3 [PO4-6-Gal]beta 1-4Man, PO4-6-GaL beta 1-3Glc beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man, PO4-6-Glc beta 1-3[PO4-6-Glc]beta 1-3[PO4-6-Gal]beta 1-4Man, PO4-6Gal beta 1-3[PO4-6-Glc]beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man, and PO4-6-Glc beta 1-3[PO4-6-Glc]beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man. These glycans are linked together by the conserved phosphodiester R-Man alpha 1-PO4-6-Gal-R or the novel phosphodiester R-Man alpha 1-PO4-6-Glc-R and are connected to Ser(P) of the protein backbone most likely via the linkage R-Man alpha 1-PO4-Ser. The variety of stage-specific glycan structures in Leishmania mexicana aPPG suggests the presence of developmentally regulated amastigote glycosyltransferases which may be potential anti-parasite drug targets.

On super-RS algebra and Drinfeld realization of quantum affine superalgebras

We describe the realization of the super-Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U-q [osp(1/2)((1))] and its degeneration - central extended super-Yangian double DY(h over bar) [osp(1/2)((1))].

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

We extend the results of spin ladder models associated with the Lie algebras su(2(n)) to the case of the orthogonal and symplectic algebras o(2(n)), sp(2(n)) where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX-type rung interactions and applied magnetic field term.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Synthesis and electrochemical properties of vanadyl phosphate di-hydrate/polyaniline derivatives hybrid films

Vanadyl phosphate and its hybrid compounds have proven to undergo electrochemical intercalation and de-intercalation of lithium ions, which enables its use as cathode material for Li ion rechargeable batteries. In this context, vanadyl phosphate di-hydrate/polyaniline derivatives hybrid films were synthesized via the exfoliation and reconstruction approach in order to evaluate their potential use as cathode in ion lithium batteries. X-ray diffraction patterns indicate that the lamellar structure of the inorganic matrix is maintained, consistent with the topotactic process. In the scanning electron micrographs, hybrid films exhibit rough surface consisting of warped and cracked crystallites, quite different from vanadyl phosphate di-hydrate square platelets crystallites. Electrochemical evaluation using cyclic voltammetry and charge-discharge galvanostatic techniques shows small differences between the charge and the discharge curves, indicating an irreversibility of the hybrid systems. (C) 2009 Elsevier B.V. All rights reserved.

Anisotropic correlated electron model associated with the Temperley-Lieb algebra

We present an anisotropic correlated electron model on a periodic lattice, constructed from an R-matrix associated with the Temperley-Lieb algebra. By modification of the coupling of the first and last sites we obtain a model with quantum algebra invariance.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.