Classical Yang-Baxter Equation and Left Invariant Affine Geometry on Lie Groups

Let G be a Lie group with Lie algebra \Cal G: = T_\epsilon G and T^*G = \Cal G^* \rtimes G its cotangent bundle considered as a Lie group, where G acts on \Cal G^* via the coadjoint action. We show that there is a 1-1 correspondance between the skew-symmetric solutions r\in \wedge^2 \Cal G of the Classical Yang-Baxter Equation in G, and the set of connected Lie subgroups of $T^*G$ which carry a left invariant affine structure and whose Lie algebras are lagrangian graphs in \Cal G \oplus \Cal G^*. An invertible solution r endows G with a left invariant symplectic structure and hence a left invariant affine structure. In this case we prove that the Poisson Lie tensor $\pi := r^+ - r^-$ is polynomial of degree at most 2 and the double Lie groups of $(G,\pi)$ also carry a canonical left invariant affine structure. In the general case of (non necessarly invertible) solutions r, we supply a necessary and suffisant condition to the geodesic completness of the associated affine structureComment: 13 pages, late

Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds

In this work it is shown that a necessary condition for the completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups, and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with non compact (local) isotropy group, those that are geodesically complete.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Labor Market Dyncamics in Chile: the Role of Terms of Trade Shocks

In this paper we explore the channels through which the terms of trade affect labor market variables in an emerging economy such as Chile. In doing so, we analyze the cyclical properties of labor market variables and use a structural vector autoregressive model to analyze the empirical responses of variables such as unemployment rate, job finding rate, sectoral employment and sectoral average labor productivity to terms of trade shocks in the case of Chile, which come from two main sources: the mining and the non-mining sector. We then develop a multi-sector model with search frictions that generates fluctuations in the unemployment rate. Using a calibrated version of this model for Chile, we analyze the ability of the model to replicate the observed responses of labor market variables to terms of trade shocks. We find that the model can predict quantitatively the effects of labor market variables to non-mining terms of trade shocks. Although the model is able to obtain responses to mining price changes qualitatively similar to what is estimated in the data, it falls short to the estimated magnitude of reduction in unemployment that follows a rise in mining prices. The presence of very high wage rigidity can help to generate a sharper fall in unemployment after a mining terms of trade rise. Finally, the model remarks a more intense sectoral labor reallocation in response to terms of trade shocks than the amount estimated in the data.

La Competitividad Exterior de la Economía Española

Las exportaciones han cobrado desde la década de los 90, y especialmente desde el año 2000 una gran importancia en el PIB de la economía española. El trabajo busca analizar el comportamiento seguido por las exportaciones desde el año 2000 al 2012 y entender las causas que han provocado que haya sido de dicha manera. En la primera parte del trabajo se hace un análisis de la oferta exportadora española desde un punto de vista agregado, donde se observa la tasa de crecimiento, la propensión a exportar, la cuota mundial y los mercados de destino. En la segunda parte del trabajo, se establece un análisis desagregado por sectores, para conocer cuales son los que mayor relevancia suponen y en qué está especializada la economía española de cara al exterior. El último apartado del trabajo trata de conclusiones y recomendaciones hechas bajo los resultados que arrojan el trabajo.Departamento de Economía AplicadaGrado en Economí