arXiv subjects
Publications and source records attributed to Elsa Fernandez.
In this paper we give a characterisation of trivial extension algebras in terms of quivers with relations. This result is based on a explicit description of the ideal of relations of the trivial extension of an algebra, given by the first author in the appendix. We also give a new proof of Wakamatsu's theorem in terms of their quiver and relations, which determines when two given algebras have isomorphic trivial extensions.
Dementia, and specially Alzheimer s disease (AD) and Mild Cognitive Impairment (MCI) are one of the most important diseases suffered by elderly population. Music therapy is one of the most widely used non-pharmacological treatment in the field of cognitive impairments, given that music influences their mood, behavior, the decrease of anxiety, as well as facilitating reminiscence, emotional expressions and movement. In this work we present HAIDA, a multi-platform support system for Musical Therapy oriented to cognitive impairment, which includes not only therapy tools but also non-invasive biometric analysis, speech, activity and hand activity. At this moment the system is on use and recording the first sets of data.
In this paper we discuss, in terms of quivers with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension two and we give a sufficient condition for it to be a quasitilted algebra. We show that this condition is not necessary. In the case of a strongly simply connected schurian algebra, we discuss necessary conditions, and, combining both type of conditions, we are able to analyze if the given algebra is quasitilted. As an application we obtain the quiver with relations of all the tilted and cluster tilted algebras of Dynkin type $E_p$.
The aim of this paper is to provide a criterion to determine, by quivers with relations, when an algebra has global dimension at most two. In order to do that, we introduce a new class of algebras of global dimension three, and we call them critical algebras. Furthermore we give a characterization of critical algebras by quivers with relations. Our main theorem states that if a strongly simply connected schurian algebra does not contain a critical algebra as a full subcategory, then it has global dimension at most two.