FERNÁNDEZ TERNERO , Desamparados

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In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This simplicial category has the property of being invariant under strong equivalences, and it only depends on the simplicial structure rather than its geometric realization. In a similar way to...

Evolution algebras are currently widely studied due to their importance not only "per se" but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A criterion for classifying those satisfying certain conditions is...

This paper is devoted to study and compare two algebraic algorithms related to the computation of Lie algebras by using statistical techniques. These techniques allow us to decide which of them is more suitable and less costly depending on several variables, like the dimension of the considered algebra.

This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n-2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case...

Although since their introduction by Tian in 2004, evolution algebras have been the subject of a very deep study in the last years due to their numerous applications to other disciplines, this study is not easy since these algebras lack an identity that characterizes them, such as the identity of Jacobi, for Lie algebras or those of Leibniz and...

We obtain the number of non-homologically equivalent excellent discrete Morse functions defined on compact orientable surfaces. This work is a continuation of the study which has been done in [2, 4] for graphs.

This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and...

In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link between graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it is isomorphic to a quotient of the positive part n+ of the KacMoody...

The simplicial LS-category of a nite abstract simplicial complex is a new invariant of the strong homotopy type, de ned in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many notions and results of alge- braic topology...

We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik– Schnirelmann theorem for general matchings on posets, in particular, for Morse–Bott functions.

We prove a version of the fundamental theorems of Morse theory in the setting of finite partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the Morse-Pitcher inequalities in that context.

The main goal of this poster, which is written in the form of a survey and tries to show some aspects of the research of authors on Lie algebras, is to pay homage to the memory of Pilar Pisón Casares, who was firstly teacher of some of them and later colleague of all of them during different stages of her stay as a member of the Departamento de...