Clifford theory for graded fusion categories

We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category graded by a group $G$ as induced from module categories over fusion subcategories associated with the subgroups of $G$. We define invariant \C_e-module categories and extensions of \C_e-module categories. The construction of module categories over \C is reduced to determine invariant module categories for subgroups of $G$ and the indecomposable extensions of this modules categories. We associate a $G$-crossed product fusion category to each $G$-invariant \C_e-module category and give a criterion for a graded fusion category to be a group-theoretical fusion category. We give necessary and sufficient conditions for an indecomposable module category to be extended.Comment: Corollary 5.5 has been corrected. Accepted by Israel Journal of Mathematic

Training mathematical skills in school children: Some preliminary results.

The present study is a further development of an earlier research on school failure. The aim is to develop sound, simple, effective evaluation and training procedures for children with difficulties to learn mathematics. A review of research on mathematical knowledge reveals some confusion in using terms and a lack of empirical studies on intervention strategies. Nevertheless, some progress has been done in defining the necessary skills for children to solve mathematical problems. In the current study, two cases of primary school children (ISCED 1) with difficulties to learn mathematics are presented. They were trained to acquire a set of pre-mathematical or mathematical skills. The core of the intervention procedures is Behavior Skills Training (BST), a highly effective technique for teaching individuals with different disabilities a wide variety of skills. Evaluation of the training is carried out by comparing the percentage of attained objectives before (pre-test) and after training (post-test). Future developments of this research are explaine

Financial Crisis and Sectoral Diversification of Argentine Banks, 1999-2004.

We explore the impact and evolution of loan portfolio diversification during the 2001-2002 Argentine financial crisis. Using a novel dataset that combines public information on the main activity of the largest 930 Argentine firms with their borrowing from each bank operating in the country during the 1999-2004 period, we find that banks did not modify much their loan portfolio mix as a response to the crisis, even though the econometric results point to a positive effect of sectoral diversification and lending to tradeable sectors on bank profitability and risk mitigation. Our results suggest that larger banks benefit more from diversification that smaller ones, and that the benefits of diversification are greater during the downside of the business cycle.Focus, Diversification, Bank risk, Bank return.