Internal labelling operators and contractions of Lie algebras

We analyze under which conditions the missing label problem associated to a reduction chain $\frak{s}^{\prime}\subset \frak{s}$ of (simple) Lie algebras can be completely solved by means of an In\"on\"u-Wigner contraction $\frak{g}$ naturally related to the embedding. This provides a new interpretation of the missing label operators in terms of the Casimir operators of the contracted algebra, and shows that the available labeling operators are not completely equivalent. Further, the procedure is used to obtain upper bounds for the number of invariants of affine Lie algebras arising as contractions of semisimple algebras.Comment: 20 pages, 2 table

A comment concerning cohomology and invariants of Lie algebras with respect to contractions and deformations

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint module. A criterion to decide whether a given deformation is invertible or not is given in dependence of the Poincar\'e polynomial.Comment: 13 pages, 1 tabl

Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements

The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on Cartan's method of moving frames.Comment: 21 pages, enhanced and extended version. Section 2 reviews the method of finding invariants of Lie algebras that was proposed in arXiv:math-ph/0602046 and arXiv:math-ph/0606045. The computation is based on developing a specific technique given in arXiv:0704.0937. Results generalize ones of arXiv:0705.2394 to the case of arbitrary relevant number of nilindependent element

International convergence and local divergence

This paper presents an East-West endogenous-growth model that reproduces recent stylized facts applicable to the trade liberalization process of many developing countries: convergence with the rest of the world, higher internal divergence, increasing spatial concentration of economic activity and higher growth rates. We claim that the ongoing reduction of manufacturing trade costs may generate a net inflow of global demand towards the industrialized cores of developing countries. This will induce a reallocation of labor from traditional to modern sectors. In turn, such a sectoral shift may enlarge the catch-up (imitation) potential of developing countries and raise global growth rates, due to Grossman and Helpman's complementarity between imitative and innovative activities. Although advanced economies may become relatively worse off, the effect on growth rates may allow them to gain in absolute terms.

Trade and Migration: a U-Shaped Transition in Eastern Europe

This paper proposes a 2-country 3-region economic geography model that can account for the most salient stylized facts experienced by Eastern European transition economies during the 1990s. In contrast to the existing literature, which has favored technological explanations, trade liberalization and factor mobility are the only driving forces. The model correctly predicts that in the first half of the decade trade liberalization led to divergence in GDP per capita, both between the West and the East and within the East. Consistent with the data, in the second half of the decade, internal labor mobility in the East reversed this process, and convergence became the dominant force. The model furthermore shows that the same U-shaped pattern applies to relative industrialization of West and East, although within the East the hinterland continued to lose industry throughout the decade.