On universal central extensions of Hom-Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.

Effects and determinants of household debt in Portugal

As the amount of debt has gradually increased, particularly in recent years, Portugal is currently one of the European countries exhibiting one of the highest levels of overall indebtedness, including in both sovereign and private sectors. Indeed, this condition is the outcome of increasing levels of debt assumed not only by the government, but also by companies and families, being the later mostly due to mortgage loans and due charges. This paper focuses on the study of borrowing by Portuguese households. The research has been made in respect to the notion of debt, the consequences of recent developments in debt, among other factors. In order to analyse the factors that are most associated with debt, a study was developed using two multiple regression models, one using a longer time series and another shorter, evaluating the effect of several variables, such as consumption, savings, unemployment, inflation and interest rates, in order to check whether they could be associated with a higher level of debt.

Cultural mega-events and the enhancement of a city's image: differences between engaged participants and attendees

A city’s image can serve as the basis upon which to develop a strong sense of community. This, in turn, fosters trust and cooperation which may attract tourists and investment, and drive regional economic growth. One strategy to enhance a city’s image is to host cultural mega-events. This study focuses on Guimarães, one of the European Capitals of Culture of 2012, and adopts a marketing communication perspective to explore issues of city image. The objective of the study reported was to understand whether images of Guimarães improved after it hosted the cultural mega-event. To attain this goal, we compare the perceptions of residents who participated in the event (engaged participants) and attendees. Several significant findings are reported and their implications for event managers and public policy administrators are presented, along with the limitations of the study.