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.

Screening of plant extracts from the Brazilian Cerrado for their in vitro trypanocidal activity

In this study we report the screening of the in vitro trypanocidal activity of 20 extracts obtained from 10 different plant species growing in the Brazilian Cerrado: Aspidosperma macrocarpum Mart. (Apocynaceae), Aegiphila sellowiano Cham. (Verbenaceae), Byrsonima intermedia Juss. (Malpighiaceae), Cyperus rotundus L. (Cyperaceae), Leandra lacunosa Cogn. (Melastomataceae), Miconia ligustroides (DC.) Naudin. (Melastomataceae), Miconia sellowiana Naudin.(Melastomataceae),Myrcia variabilis Mart.ex DC. (Myrtaceae), Solanum lycocarpum St. Hil. (Solanaceae), and Tibouchina stenocarpa Cogn. (Melastomataceae). The most active extracts were submitted to phytochemical analyses. High-resolution gas chromatography analysis of the n-hexane extract of T. stenocarpa (IC(50) = 23.6 mu g/mL), the most active extract amongst all the tested samples, allowed the identification of beta-amyrin, alpha-amyrin, lupeol, friedelin, beta-friedelanol, campesterol, stigmasterol, and beta-sitosterol. Oleanolic and ursolic acids were isolated from the methylene chloride extract of T stenocarpa (IC(50) = 51.5 mu g/mL), while ursolic acid was isolated from the methylene chloride extract of M. variabilis (IC(50)=38.4 mu g/mL). Solasonine and solamargine were identified as major compounds by mass spectrometry analysis in the hydroalcoholic extract of the fruits of S. lycocarpum (IC(50)=57.1 mu g/mL).The results showed that the trypanocidal activity may be related to the major compounds identified in the crude active extracts.

Cytotoxic and mutagenic evaluation of extracts from plant species of the Miconia genus and their influence on doxorubicin-induced mutagenicity: An in vitro analysis

The Miconia genus, a plant widely used for medicine, occurs in tropical America and its extracts and isolated compounds have demonstrated antibiotic, antitumoral, analgesic and antimalarial activities. However, no study concerning its genotoxicity has been conducted and it is necessary to determine its potential mutagenic effects to develop products and chemicals from these extracts. This study assessed the cytotoxicity, mutagenicity and the protective effects of methanolic extracts from Miconia species on Chinese hamster lung fibroblast cell cultures (V79). The cytotoxicity was evaluated using a clonogenic assay. Cultures exposed to the extract of Miconia albicans up to a concentration of 30 mu g/mL, M. cabucu up to 40 mu g/mL, M. albicans up to 40 mu g/mL and M. stenostachya up to 60 mu g/mL exhibited a cytotoxic effect on the cells. The clonogenic assay used three non-cytotoxic concentrations (5, 10 and 20 mu g/mL) to evaluate mutagenicity and antimutagenicity of the extracts. Cultures were treated with these three extract concentrations (mutagenicity test) or the extract associated with doxorubicin (DXR) (antimutagenicity test) in three protocols (pre-, simultaneous and post-treatments). Distilled water and DXR were used as negative and positive controls, respectively. In the micronucleus (MN) test, a significant reduction was observed in MN frequency in cultures treated with DXR and extracts compared to those receiving only DXR; a significant reduction was also observed for the presence of mutagenicity in all treatments. This study confirmed the safe use of Miconia extracts at the concentrations tested and reinforced the therapeutic properties previously described for Miconia species by showing their protective effects on doxorubicin-induced mutagenicity. (C) 2010 Elsevier GmbH. All rights reserved.

Twisted parafermions

A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted Z-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra A(2)((2)) is given.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

The q-deformed supersymmetric t-J model with a boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U-q[sl(2\1)]. We. give the bosonization of the boundary states. We give an integral expression for the correlation functions of the boundary model, and derive the difference equations which they satisfy.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.

Free field and parafermionic realizations of twisted su(3)(k)((2)) current algebra

Free field and twisted parafermionic representations of twisted su(3)(k)((2)) current algebra are obtained. The corresponding twisted Sugawara energy-momentum tensor is given in terms of three (beta, gamma) pairs and two scalar fields and also in terms of twisted parafermionic currents and one scalar field. Two screening currents of the first kind are presented in terms of the free fields.

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.