Guillermo Vera de Salas

Rey Juan Carlos University | URJC · Applied Mathematics

En este trabajo introducimos el álgebra de cuaternios ℍ. Desde la teoría del álgebra lineal, construimos las matrices asociadas a ciertos endomorfismos en ℍ que se identificarán con rotaciones en ℝ3, para acabar con un ejemplo práctico de como describir el movimiento de un brazo robótico en términos de cuaternios.

A R T I C L E I N F O Dataset link: https://github.com/LaComarca-La b/HyperGraph-Communities Keywords: Hypergraph Derivative of a hypergraph Higher-order network Community Communities in a hypergraph UPGMA Hierarchical clustering A B S T R A C T Similar to what happens in the pairwise network domain, the communities of nodes of a hypergraph (also c...

Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel matrices whose entries satisfy a second-order lin...

Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel matrices whose entries satisfy a second order lin...

An element a is nilpotent last-regular if it is nilpotent and its last nonzero power is von Neumann regular. In this paper we show that any nilpotent last-regular element a in an associative algebra R over a ring of scalars Φ gives rise to a complete system of orthogonal idempotents that induces a finite Z-grading on R; we also show that such eleme...

In this paper, we study ad-nilpotent elements of semiprime rings R with involution \(*\) whose indices of ad-nilpotence differ on \({{\,\mathrm{Skew}\,}}(R,*)\) and R. The existence of such an ad-nilpotent element a implies the existence of a GPI of R, and determines a big part of its structure. When moving to the symmetric Martindale ring of quoti...

In this paper we give an in-deph analysis of the nilpotency index of nilpotent homogeneous inner superderivations in associative prime superalgebras with and without superinvolution. We also present examples of all the different cases that our analysis exhibits for the nilpotency indices of the inner superderivations.

In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R, we introduce a more restrictive notion of ad-nilpotent element, pure ad-nilpotent element, which is a only technical condition since every ad-nilpotent element can be ex...

Given a Lie superalgebra and an even ad-nilpotent element of index ≤3, one can obtain a Jordan superalgebra attached to that element; inspired by that construction we build a Jordan superpair attached to an odd ad-nilpotent element of index ≤4. We introduce inner ideals for Lie superalgebras, and we prove that the associated subquotients are Jordan...

In this paper we give an inductive new proof of the Jordan canonical form of a nilpotent element in an arbitrary ring. If a∈R is a nilpotent element of index n with von Neumann regular an−1, we decompose a=ea+(1−e)a with ea∈eRe≅Mn(S) a Jordan block of size n over a corner S of R, and (1−e)a nilpotent of index <n for an idempotent e of R commuting w...