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.

Residents’ perspectives on tourism impacts of portuguese world heritage historic centers: Angra do Heroísmo and Évora

The aim of this study is twofold. First, the study analyzes local community perspectives of the importance of the World Heritage Site (WHS) classification of the historic centers of Angra do Heroísmo and Évora. Second, the study analyzes local residents’ perceived tourism impacts on the municipalities of Angra do Heroísmo and Évora. The methodology comprises quantitative research based on a self-administered survey applied to convenience samples of local residents of the two Portuguese municipalities in 2014. The main results reveal that local residents have a strongly positive perception of the WHS designation in both municipalities. With regard to the perceived tourism impacts, residents from Angra do Heroísmo have a stronger agreement about the impacts of tourism on their city than the residents of Évora, except for the negative social and cultural impacts. The comparison of the mean scores of these impacts across residents that live near and far from the historic centers reveals that the most valued and least valued impacts in the three categories of impacts (economic, social and cultural, and environmental) are common to all groups of residents. Nevertheless, residents living in or near the historic center of Angra do Heroísmo have higher means in the majority of tourism impacts (in all categories), with only one negative impact to concern the majority of respondents. Among the residents from Évora, residents living in or near the historic center have higher means in the majority of economic impacts but lower means in almost social and cultural impacts. With regard to the environmental impacts, residents living in or near the historic center have higher means scores in the positive impacts and lower means scores in the negative environmental impacts.