Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra

In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever-Novikov type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra, the Virasoro algebra, the classical current, and the affine Kac-Moody Lie algebras respectively. The constructed families are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid. This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The algebras are of relevance in the global operator approach to the Wess-Zumino-Witten-Novikov models appearing in the quantization of Conformal Field Theory.Comment: 17 page

Quasi-classical Lie algebras and their contractions

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras.Comment: 17 pages, 2 Table

Contractions, deformations and curvature

The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework. We show that a given Lie algebra contraction can be interpreted geometrically as the zero-curvature limit of some underlying homogeneous space with constant curvature. In particular, we study in detail the contraction process for the three classical Riemannian spaces (spherical, Euclidean, hyperbolic), three non-relativistic (Newtonian) spacetimes and three relativistic ((anti-)de Sitter and Minkowskian) spacetimes. Next, from a different perspective, we make use of quantum deformations of Lie algebras in order to construct a family of spaces of non-constant curvature that can be interpreted as deformations of the above nine spaces. In this framework, the quantum deformation parameter is identified as the parameter that controls the curvature of such "quantum" spaces.Comment: 17 pages. Based on the talk given in the Oberwolfach workshop: Deformations and Contractions in Mathematics and Physics (Germany, january 2006) organized by M. de Montigny, A. Fialowski, S. Novikov and M. Schlichenmaie

An item-level examination of the Flynn effect on the National Intelligence Test in Estonia

This study examined the Flynn effect (FE; i.e., the rise in IQ scores over time) in Estonia using the Estonian version of the National Intelligence Tests (NIT; Haggerty et al., 1919 and National Research Council, 1920). Using secondary data from two cohorts (1934, n = 890 and 2006, n = 913) of students, we analyzed the NIT's subtests using item response theory (IRT). For each subtest, we first examined invariance in all the items and then linked the latent variable (θ) scores between the two cohorts using the invariant items. The results showed that there was a FE in θ for all subtests except one, although there was much variability in the FE magnitude, ranging from an effect size of 0.24 (3.60 IQ points) to 1.05 (15.75 IQ points). In addition, this study showed there was a decrease in the variability of θ for all the subtests, although only two of the subtests showed large decreases (approximately .50 standard deviations). Last, the subtests' precision of measuring θ was very similar at both time points

Spearman's hypothesis tested comparing Libyan adults with various other groups of adults on the items of the Standard Progressive Matrices

Spearman's hypothesis tested at the level of items states that differences between groups on the items of an IQ test are a function of the g loadings of these items, such that there are small differences between groups on items with low g loadings and large differences between groups on items with high g loadings, and it has been confirmed in a limited number of studies. In this paper, we tested Spearman's hypothesis, comparing groups of Libyan university students and adults with comparable groups from South Africa, Spain, and Russia, and a group of Roma (Gypsies) from Serbia (total N = 844). The analyses were carried out on comparisons between the Libyans and the other groups. Spearman's hypothesis was strongly confirmed with a mean weighted r with a value of .73. We conclude that Spearman's hypothesis tested at the item level appears to be a more regular phenomenon than previously thought

Spearman's hypothesis tested comparing Libyan secondary school children with various other groups of secondary school children on the items of the Standard Progressive Matrices

Spearman's hypothesis tested at the level of items states that differences between groups on the items of an IQ test are a function of the g loadings of these items, such that there are small differences between groups on items with low g loadings and large differences between groups on items with high g loadings, and it has been confirmed in a limited number of studies. In this paper, we tested Spearman's hypothesis, comparing a group of Libyan secondary school children (N = 1080) with other groups of secondary school children from Bosnia and Herzegovina, Estonia, Ukraine, Russia, South Africa, Ireland, and Chile (total N = 7476). The analyses were carried out on 9 comparisons between the Libyan children and the other children. Spearman's hypothesis was strongly confirmed with a mean weighted r with a value of .61. We conclude that Spearman's hypothesis tested at the item level appears to be a more regular phenomenon than previously thought