arXiv subjects

Raúl Felipe

Publications and source records attributed to Raúl Felipe.

4 recordsLinked to original sources

arXiv2025

Associative triple trisystems and standard embeddings

Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of di-endomorphisms of any module, which enables the construction of the standard embedding for any associative triple trisystem.

math.RA↗

arXiv2023

Operations on the set of scalar and matrix-valued quiddity sequences

Our purpose with this paper is, in first place, to recast the space of quiddity sequences corresponding to usual frieze patterns as a different type of SET operad, and second to introduce and study $\mathfrak{M}$-quiddity sequences where $\mathfrak{M}$ is a monodromy block matrix of order two. Also, we examine some related topic as are the possibility of to define matrix-valued friezes patterns and noncommutative signed Chebyshev polynomials.

math.CO↗

arXiv2022

New composition products for complex harmonic functions, the dynamic with respect to these and composition operators induced

In this work we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here we begin the study of the iterations of the functions of this class showing briefly their potential to be a topic of future research. In parallel, we define and study composition operators whose symbols belong to a Hardy space of complex harmonic functions also introduced in the work. All this constitutes a previous work for the research of semigroups and evolutionary families composed of complex harmonic functions.

math.CV↗

arXiv2020

Lattice Diversities

Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the concept of a diversity tight span that extends the metric tight span in a natural way. Here we explore the generalization of diversities to lattices. Instead of defining diversities on finite subsets of a set we consider diversities defined on members of an arbitrary lattice (with a 0). We show that many of the basic properties of diversities continue to hold. However, the natural map from a lattice diversity to its tight span is not a lattice homomorphism, preventing the development of a complete tight span theory as in the metric and diversity cases.

math.MG↗