Esther García

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20112026

most citedDecomposition of matrices into a sum of invertible matrices and matrices of fixed index

3 citations · 5 across the 5 of their papers we have counts for

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math.RA2026

Leibniz algebras and their connection to Jordan pair disystems

Esther García, Miguel Gómez Lozano, Rubén Muñoz Alcázar +1

In this paper we present a generalization of Jordan pairs, called Jordan pair disystem, which appear naturally as the wings of a Leibniz algebra with a finite $Z$ -grading;…

math.RA2023★ 2 cited

Decompositions of Matrices Into a Sum of Torsion Matrices and Matrices of Fixed Nilpotence

Peter Danchev, Esther García, Miguel Gómez Lozano

For $n \geq 2$ and fixed $k \geq 1$ , we study when a square matrix $A$ over an arbitrary field $F$ can be decomposed as $T + N$ where $T$ is a torsion matrix and $N$ is a nilpot…

math.RA2023★ 3 cited

Decomposition of matrices into a sum of invertible matrices and matrices of fixed index

Peter Danchev, Esther García, Miguel Gómez Lozano

For any $n \geq 2$ and fixed $k \geq 1$ , we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring $M_{n} (F)$ to be written…

math.RA2021

Decompositions of Matrices into Potent and Square-Zero Matrices

Peter Danchev, Esther Garcia, Miguel Gomez Lozano

In order to find a suitable expression of an arbitrary square matrix over an arbitrary finite commutative ring, we prove that every such a matrix is always representable as a sum o…

math.RA2011

Abelian gradings in Lie algebras

Esther Garcia, Miguel Gomez Lozano

Given a Lie algebra $L$ graded by a group $G$ , if $L$ is does not contain orthogonal graded ideals and $G$ is generated by the support of $L$ , then $G$ is an abelian group.