Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

On simple Lie algebras over a field of characteristic 2

We prove that the simple Lie algebras constructed by G. Jurman (2004) in 121 are isomorphic to Hamiltonian algebras. As a corollary we answer all questions formulated in G. Jurman (2004) [2] about isomorphisms of these algebras. (C) 2012 Elsevier Inc. All rights reserved.

The correlation between the phenolic composition and biological activities of two varieties of Brazilian propolis (G6 and G12)

Biological assays that have been performed on different types of Brazilian propolis have shown that type 6 propolis (G6) has a strong antimicrobial activity and a low flavonoid content. This study aimed to evaluate the correlation between the phenolic composition and the biological activities displayed by propol is G6 from the state of Bahia and green propol is, also known as type 12 (G12). The values of the flavonoids and the total phenolics in propol is G6 were different than those in propolis G12. Although the G12 variety presented greater antioxidant activity, propolis G6 proved to have greater antimicrobial and cytotoxic activities. The results showed that the phenolic compounds may not be the only compounds responsible for the biological activity. More detailed studies of the chemical composition and an assessment or the biological activity are required to establish the quality of propolis.

A comparative study of the thermoluminescence properties of several varieties of Brazilian natural quartz

The following varieties of natural quartz, as the blue, the green, the red, the pink, the black, the sulphurous and the milky quartz, have been investigated concerning their thermoluminescence properties. For comparison sake natural colorless alpha quartz has been include. Since X-rays diffraction analysis has shown that all of them have the same crystal structure as the alpha quartz, it is expected that no great change in the TL property should be found, however, that was not the case. The TL peaks at 110, 175, 220, 325 and 375 degrees C observed in the alpha quartz are not found in all the varieties of quartz, for instance, the sulphurous quartz presented only 110 degrees and 245 degrees peaks, the pink one presented just 110, 220 and 375 degrees C peaks and so on. In respect to TL response as function of gamma ray dose a quite varied behavior has been observed and discussed. (C) 2012 Elsevier B.V. All rights reserved.

Physical and chemical characterization of the pulp of different varieties of avocado targeting oil extraction potential

The aim of this study was to evaluate the physicochemical properties of avocado pulp of four different varieties (Avocado, Guatemala, Dickinson, and Butter pear) and to identify which has the greatest potential for oil extraction. Fresh avocado pulp was characterized by moisture, protein, fat, ash, carbohydrates and energy contents were determined. The carotenoids and chlorophyll contents were determined by the organic solvent extraction method. The results showed significant differences in the composition of the fruit when varieties are compared. However, the striking feature in all varieties is high lipid content; Avocado and Dickinson are the most suitable varieties for oil extraction, taking into account moisture content and the levels of lipids in the pulp. Moreover, it could be said that the variety Dickinson is the most affected by the parameters evaluated in terms of overall quality. Chlorophyll and carotenoids, fat-soluble pigments, showed a negative correlation with respect to lipids since it could be related to its function in the fruit. The varieties Avocado and Dickinson are an alternative to oil extraction having great commercial potential to be exploited thus avoiding waste and increasing farmers income.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

On delta-derivations of n-ary algebras

We give a description of delta-derivations of (n + 1)-dimensional n-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial delta-derivations of Filippov algebras and show that there are no non-trivial delta-derivations of the simple ternary Mal'tsev algebra M-8.

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

Symmetry insights for design of supercomputer network topologies: roots and weights lattices

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

delta-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras

In the paper, a complete description of the delta-derivations and the delta-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic p not equal 2 is given. In particular, new examples of nontrivial (1/2)-derivations and odd (1/2)-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

Antioxidative responses of cell suspension cultures of two Coffea arabica varieties to low aluminum levels at pH 5.8

The effects of aluminum (Al) on the activities of antioxidant enzymes and ferritin expression were studied in cell suspension cultures of two varieties of Coffea arabica, Mundo Novo and Icatu, in medium with pH at 5.8. The cells were incubated with 300 µM Al3+, and the Al speciation as Al3+ was 1.45% of the mole fraction. The activities of superoxide dismutase (SOD), catalase (CAT), and glutathione S-transferase (GST) were increased in Mundo Novo, whereas glutathione reductase (GR) and guaiacol peroxidase (GPOX) activities remained unchanged. SOD, GR, and GST activities were increased in Icatu, while CAT activity was not changed, and GPOX activity decreased. The expression of two ferritin genes (CaFer1 and CaFer2) were analyzed by Real-Time PCR. Al caused a downregulation of CaFER1 expression and no changes of CaFER2 expression in both varieties. The Western blot showed no alteration in ferritin protein levels in Mundo Novo and a decrease in Icatu. The differential enzymes responses indicate that the response to Al is variety-dependent.

Contrasted crustal sources as defined by whole-rock and Sr-Nd-Pb isotope geochemistry of neoproterozoic early post-collisional granitic magmatism within the Southern Brazilian Shear Belt, Camboriu, Brazil

The early phase of post-collisional granitic magmatism in the Camboriu region, south Brazil, is represented by the porphyritic biotite +/- hornblende Rio Pequeno Granite (RPG; 630-620 Ma) and the younger (similar to 610 Ma), equigranular, biotite +/- muscovite Serra dos Macacos Granite (SMG). The two granite types share some geochemical characteristics, but the more felsic SMG constitutes a distinctive group not related to RPG by simple fractionation processes, as indicated by its lower FeOt, TiO2, K2O/Na2O and higher Zr Al2O3, Na2O, Ba and Sr when compared to RPG of similar SiO2 range. Sr-Nd-Pb isotopes require different sources. The SMG derives from old crustal sources, possibly related to the Paleoproterozoic protoliths of the Camboriu Complex, as indicated by strongly negative epsilon Nd-t (-23 to -24) and unradiogenic Pb (e.g., Pb-206/Pb-204 = 16.0-16.3; Pb-207/Pb-204 = 15.3-15.4) and confirmed by previous LA-MC-ICPMS data showing dominant zircon inheritance of Archean to Paleoproterozoic age. In contrast, the RPG shows less negative epsilon Nd-t (-12 to -15) and a distinctive zircon inheritance pattern with no traces of post-1.6 Ga sources. This is indicative of younger sources whose significance in the regional context is still unclear; some contribution of mantle-derived magmas is indicated by coeval mafic dykes and may account for some of the geochemical and isotopic characteristics of the least differentiated varieties of the RPG. The transcurrent tectonics seems to have played an essential role in the generation of mantle-derived magmas despite their emplacement within a low-strain zone. It may have facilitated their interaction with crustal melts which seem to be to a large extent the products of reworking of Paleoproterozoic orthogneisses from the Camboriu Complex. (C) 2012 Elsevier Ltd. All rights reserved.

CHARACTERIZATION STUDY OF CAMBUCI FRUIT [Campomanesia phaea (O. Berg.) Landrum] AND ITS APPLICATION IN JELLY PROCESSING

CHARACTERIZATION STUDY OF CAMBUCI FRUIT [Campomanesia phaea (O. Berg.) Landrum] AND ITS APPLICATION IN JELLY PROCESSING The objective of this paper was to study possible differences of varieties of cambuci fruit reported by producers by means of fruit characterization and elaboration of jelly. The fruits were divided in four possible varieties groups, named as A, B, C and D, and submitted to analysis regarding weight, ash, moisture, pH, soluble solids, acidity, ratio, ascorbic acid and water activity. To the preparation of the jelly was chosen the variety A with two formulations, 50%50% and 40%60%, fruit and sugar respectively. Concerning the possible varieties of cambuci only water activity was not significantly different. The acidity and ratio of B variety are noteworthy, because it did differ from the others presenting a more satisfactory result for in natura consumption. All other tests presented statistic alteration of at least one variety, but since these data can be influenced by edaphoclimatic conditions they must be carefully observed. Lower results for pH, acidity, luminosity and degrees hue, were observed for the 60% sugar jelly sample, which contributed for its better results in the preference test for the attributes appearance, color, flavor and texture. The evaluation of attribute aroma of both samples (50% and 60%) did not differ.

Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension <400 with new identities correspond to partitions 2(5), 1 and 2(4), 1(3) and have dimensions 132 and 165. We construct an explicit new multilinear identity for partition 2(5), 1 and we demonstrate the existence of a new non-multilinear identity in which the underlying variables are permutations of a(2)b(2)c(2)d(2)e(2) f.