Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform

Using the Moyal *-product and orthosymplectic supersymmetry, we construct a natural non trivial supertrace and an associated non degenerate invariant supersymmetric bilinear form for the Lie superalgebra structure of the Weyl algebra. We decompose adjoint and twisted adjoint actions. We define a renormalized supertrace and a formal inverse Weyl transform in a deformation quantization framework and develop some examples.Comment: 26 pages; v1: added a reference, corrected typos; v2: changed title, added a reference, typos fixe

Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).Comment: 11 pages, to be published in Letters in Mathematical Physics; added references, corrected typo

Lie algebras generated by extremal elements

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.Comment: 28 page

Female - headed households, poverty, and the welfare of children in urban Brazil

The authors analyze the characteristics and behavior of households headed by women in urban Brazil and identify some of the consequences for child welfare on the growth of these households. The following was among their findings. First, households headed by women are a heterogeneous group, which varies strongly by region - as does the extent of poverty among them. Such households are more common in the northeast and increase with urbanization. Second, households headed by women are not, on average, a"vulnerable group"in Brazil, as some are quite well off. The subset of such households that are very poor is quite vulnerable. Households headed by women tend to be poorer in the northeast, especially around Recife, than in Porto Alegre in the south, where there is virtually no gap. Third, less than half the households headed by women contain dependent children, and only a third are headed by the stereotypical"single mother."When there are children in households headed by women, especially households headed by single mothers, the income gap is greater than in other households. As a portion of households in Brazil, households headed by women and containing children represent only 3.4 percent of urban households, but this group tends to be poor, which is worrisome for child outcomes. Poor children tend to live in households headed by women. These households are poor not because there are more children or fewer adults but because women earn less than men. Women heading households do not earn less than other women - on the contrary. However, it female heads of households earned as much as male heads of households, the average income in households headed by women would be above that for other households and fewer single mothers would be poor. The best interventions toeliminate poverty in this group are those that focus on: (a) ending wage discrimination; and (b) ending occupational segregation. Interventions that focus on raising skill levels and educational attainment for the whole workforce, including women, would also help alleviate absolute poverty, although not necessarily relative income differences."Workfare"or public employment policies would not help this group since most already participate in the labor force. Programs targeted to this group would not be particularly progressive, given the heterogeneity and income spread among these households. But the results do suggest the need for special interventions for children in households headed by women, given those children's tendency to stay out of school.Poverty Assessment,Anthropology,Town Water Supply and Sanitation,VN-Acb Mis -- IFC-00535908,Housing&Human Habitats

Plan stratégique

Este artigo aborda o uso indiscriminado da medida de proteção Abrigos para Adolescentes, na cidade de Santa Maria, mostrando as dificuldades na transição das antigas orientações da política de atendimento à criança e ao adolescente para a indicada pelo Estatuto da Criança e do Adolescente (ECA). Sugere um amplo debate e urgente revisão com todos os envolvidos no processo de encaminhamento e acolhimento de adolescentes aos abrigos municipais, para que este seja um efetivo espaço social de proteção para aqueles que necessitam de apoio fora do contexto familiar e comunitári