POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.

Lie properties of crossed products

Let F-sigma(lambda)vertical bar G vertical bar be a crossed product of a group G and the field F. We study the Lie properties of F-sigma(lambda)vertical bar G vertical bar in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie (n, m)-Engel. (C) 2008 Elsevier Inc. All rights reserved.

Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

A Characterization of Varieties of Associative Algebras of Exponent two

∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

[the Sociology Of Health In Brazil - The Creation Of An Identity].

This article analyzes the historical, social and cognitive dimensions of the sociology of medicine in the construction of its identity, from Wolf Lepenies' perspective. It is understood that the construction of an identity does not end with the first historical manifestations, but is consolidated when it is institutionalized and structured as a field of knowledge by creating its own forms of cognitive expression. The text is divided into three parts: in the first the precursors are presented, highlighting the role played by some travelers, naturalists and folklore scholars, followed by social physicians-scientists and the first social scientists (1940-1969). In the second part, aspects of the consolidation of the social sciences in health are presented at two significant moments, namely the 1970s and 1980s. In the third part, the issues raised by the field are addressed in general terms. It is considered that once the main structural stages are in place there is still a need for the formation of new generations of social scientists in health. It is also essential to disseminate scientific production and to ensure that the relations are studied in depth and institutionalized with the sociological matrices on the one hand and with the field of health on the other.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Evaluating the Taxonomic Identity in Four Species of the Lobose Testate Amoebae Genus Arcella Ehrenberg, 1832

The taxonomic identity in microbial eukaryotes remains an impediment to discussing ecology, biogeography and phylogeny, mainly due to a lack of standards in organism descriptions and few comparative works. The lobose testate amoebae (Arcellinida) present an ideal study system, as progress is severely hindered due to taxonomic confusion. In the present survey, we have examined the morphology, biometry and ecology of 2400 individuals in the genus Arcella Ehrenberg, 1832, collected from the Tiete River in Sao Paulo, Brazil. We then contrasted these new data with 26 previously described species, varieties and forms, looking for consistencies and trying to establish distinct entities. Using a combination of morphology and multivariate statistics we were able to determine 4 distinct taxa (Arcella hemisphaerica, Arcella discoides, Arcella gibbosa and Arcella brasiliensis), each of them encompassing a number of other non-distinct nominal taxa. We describe in detail each of the 4 taxa with notes on ecology and biogeography, and list the indistinguishable names in an effort to make identification and taxonomy in the testate amoebae a more objective and precise exercise by clarifying the taxonomic identity.

Strongyloides venezuelensis: The antigenic identity of eight strains for the immunodiagnosis of human strongyloidiasis

The antigens of eight strains of Strongyloides venezuelensis were identified by means of the indirect immunofluorescence antibody (IFAT), enzyme-linked immunosorbent assay (ELISA) and immunoblot (IB) tests. Infective larvae (L3) from these strains were obtained from Rattus norvegicus feces cultures. For IFAT, sections of U were used while the ELISA and IB, tests were conducted with alkaline extract. Ninety serum samples were tested: 30 from patients with S. stercoralis, 30 from patients with other parasitic diseases, and 30 from healthy subjects (free of parasites). Average sensitivity and specificity among all eight strains, both for IFAT and ELISA, were, respectively, 93% and 100%. In the IB, anti-S. stercoralis IgG recognized a single antigenic fraction with 45 kDa. Serum samples from patients with S. stercoralis revealed antigens from different strains of S. venezuelensis, indicating antigenic identity for possible use in the synthesis of recombinant antigen that could be useful in immunodiagnosis and vaccine against this parasite. (C) 2008 Elsevier Inc. All rights reserved.

(FAB12_2_019) National identity at Arakawa & Gins’ Site of Reversible Destiny—Yoro, Japan

This paper examines the manipulation of forms of the traditional Japanese stroll garden at Site of Reversible Destiny, a tourist park designed by the New Yorkbased collaborators Shusaku Arakawa and Madeline Gins. Landscape and its representations are central to the construction of national identity in Japan since the cultural distinctiveness of the Japanese people has been argued to rest on their unique relationship to nature and the country’s idiosyncratic geography. The stroll garden of the larger estates and palaces of the Edo period (1615–1867) developed out of earlier temple gardens and most public parks in contemporary Japan are in the grounds of these historic sites or reproduce their forms.