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.

Vernacular meaning making : Examples of narrative impact in fiction film questioning the 'banal' notion in mediatization of religion theory

The outcome of an audience study supports theories stating that stories are a primary means by which we make sense of our experiences over time. Empirical examples of narrative impact are presented in which specific fiction film scenes condense spectators' lives, identities and beliefs. One conclusion is that spectators test the emotional realism of the narative for greater significance, connecting diegetic fiction experiences with their extra-diegetic world in their quest for meaning, self and identity. The 'banal' notion of the mediatization of religion theory is questioned as unsatisfactory in the theoretical context of individualized meaning-making processes. As a semantically negatively charged concept, it is problematic when analyzing empirical examples of spectators' use of fictional narratives, especially when trying to characterize the idiosyncratic and complex interplay between spectators' fiction emotions and their testing of mediated narratives in an exercise to find moral significance in extra-filmic life. Instead vernacular meaning-making is proposed.

Constructing meanings and identities in child protection practice

Examines a contemporary and contentious social problem, child maltreatment, and the policy and practice in response to it, child protection.

Corners, squares and urban identities: perceptions, attitudes and values

In February 2000, the new Victorian Labor Government announced that they were removing the western shard from Lab Architecture Studio's winning Melbourne Federation Square design. then under construction. The specific 'contested terrain' at the intersection of Flinders Street and Swanston Street Walk. Melbourne, allows the exploration of the politics of place construction over time, through an examination of Young and Jackson's Hotel [1861]. St Paul's Cathedral [1886). Flinders Street Station [1912]. the Westin Hotel [1999) and Federation Square. This site brings together architectural and social history, questions public space and identity, and looks at Melburnian's perceptions, attitudes and values. It further demonstrates that the fragmentation of the professions, and fragmentary histories. lead to the preservation of 'bits' of architecture and the destruction of the urban/landscape context, jeopardizing the Identity of place.