Skew-symmetric identities of octonions

Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skew-symmetric identities and central polynomials of octonions are classified. (C) 2008 Elsevier B.V. All rights reserved.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

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.

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.

ASSOCIATIVE IDENTITIES OF OCTONIONS

We work to find a basis of identities for an octonion algebra modulo an associator ideal of a free alternative algebra, or, in other words, a basis for an associative replica of an ideal of identities of an octonion algebra.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Group identities on symmetric units

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.

Alternative Identities and Foreign Language Learning

My D-essay has the working title “Alternative Identities and Foreign Language Learning”. I have chosen this area because I have noticed a certain reluctance among Swedish students to use the foreign language English in English classes. They often seem embarrassed to express themselves in a language which is not their mother tongue, but they seem less embarrassed when they are allowed to act somebody else. These two observations converge into a focus of discussion on the matter, which will be supported by a minor study of my own, by extracts from other people’s essays on the matter, and by an overview of current litterature on language, identity and drama.The aim of my essay is to compare Swedish students’ willingness to use the foreign language English when acting minor plays in school, as themselves and as a chosen character, and to investigate the possibility of improving students’ willingness to use a foreign language, when given the opportunity to do so through acting somebody else.

"I'm still here. Sort of." : Constructed Identities in Paul Auster's City of Glass

Paul Auster’s City of Glass contains a jumble of identities. In fact, the identities are more numerous than the characters, and consequently, characters have several different identities. Some of these identities are obvious constructs, but with others the degree of construction is less evident. Poststructuralist theory, however, puts forward the idea that these seemingly original identities are in fact constructs to the same level as all others. Thus, this essay argues that there are no original identities; identities are constructed by outer factors. This essay discusses three outer factors contributing to the construction of identities, factors commonly discussed in poststructuralist criticism, these three being language, cultural codes and chance.

Racial Conflict in the United States of America : A Deconstructive Perspective on Native Speaker by Changrae Lee

Written about the time of the Golden Venture incident, Chang-rae Lee’s Native Speaker makes a particular reference to that incident, whereby implying that particular immigrants, on the grounds of their racial identities, are mistreated and considered as aliens by some Americas. While some whites discriminate against immigrants, there is widespread ethnic tension between Korean Americans and African Americans. Significantly, racial conflict between Koreans and blacks and the racist attitude of some whites toward immigrants are mirrored in the relationship between the Korean-American protagonist Henry and his American wife Lelia. That is, due to their different racial identities they do not understand each other and they always argue. However, toward the end of the novel, Henry and Lelia come to understand each other. While ethnic conflict between Koreans and blacks and certain whites’ discriminatory attitudes toward immigrants is serious one, the novel suggests the unimportance of racial identity. In other words, the novel concludes that there is no discriminatory treatment of immigrants and, in fact, every one is a native Speaker in America. In the novel there is no message of how racial conflict could be resolved. However, this essay suggests that by investigating how the tension between Henry and Lelia is resolved, one could suggest a solution for the ethnicity problem in America and in real life.

Projekt Norrliden : Om småstadspressens etnifiering och genderisering av en förort

The Norrliden project. Genderisation and ethnification of a low status residential area in the local press Media often contributes to segregation by constructing low status residential areas as “different” from what is “normal” and “Swedish”. Research into media representations of these residential areas often focuses big city contexts. Furthermore, research tends to be preoccupied with the construction of ethnic differences, paying little attention to the relationship between construction processes of gender and ethnicity. This article is a critical analysis of how the local daily newspapers in a medium sized town, Kalmar, construct stereotypes of immigrants and gendered identities in the low status residential area Norrliden. Two newspapers were studied in search for articles related to the area, published during the year 2005. Despite the newspapers’ claim that they want to contribute to a more nuanced and less stereotyped image of the residential area the consequences of their work seem to be the opposite. The representation sof the area are coded with stereotypes suggesting that the area is unsafe and dangerous and that the people who live there are motivated by affect and emotions rather than by successful socialisation. These representations are also characterised by notions of ethnicity and gender, as well as class. Norrliden is described as an area in need of change and improvement, as an unfinished project dependent upon aid from the outside. A reading of the 2005 media representations of Norrliden exposes an example of “symbolic violence” in that texts and photographs repeatedly degrade the area and its inhabitants.