arXiv subjects

Alejandra S. Córdova-Martínez

Publications and source records attributed to Alejandra S. Córdova-Martínez.

6 recordsLinked to original sources

arXiv2026

Automorphism group schemes of Kantor pairs of associative central simple structurable algebras

In this work, a description of the automorphism group schemes is given for the Kantor pairs (and for some Kantor triple systems related to them) associated to associative central simple structurable algebras in the three ``split'' cases, where the base field is algebraically closed of characteristic different from $2$. For two of the three cases (the ones with orthogonal and symplectic involutions), we relate the decomposition (as a central product) of the automorphism group scheme to a decomposition (as a tensor product) of the corresponding Kantor pair regarded as a metric generalized Jordan pair.

math.RA↗

arXiv2026

Alternating and symmetric superpowers of metric generalized Jordan superpairs

The aim of this paper is to define and study the constructions of alternating and symmetric (super)powers of metric generalized Jordan (super)pairs. These constructions are obtained by transference via the Faulkner construction. The construction of tensor (super)products for metric generalized Jordan (super)pairs is revisited. We always assume that the characteristic of the base field $\mathbb{F}$ is different from $2$; in case of positive characteristic, sometimes we require that the characteristic is large enough to allow nondegeneracy of certain bilinear forms.

math.RA↗

arXiv2023

Short (SL2xSL2)-structures on Lie algebras

S-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2xSL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J-ternary algebras of Allison, endowed with a nontrivial idempotent.

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arXiv2020

Fine gradings on Kantor systems of Hurwitz type

We give a classification up to equivalence of the fine group gradings by abelian groups on the Kantor pairs and triple systems associated to Hurwitz algebras (i.e., unital composition algebras), under the assumption that the base field is algebraically closed of characteristic different from 2. The universal groups and associated Weyl groups are computed. We also determine, in the case of Kantor pairs, the induced (fine) gradings on the associated Lie algebras given by the Kantor construction.

math.RA↗

arXiv2019

Gradings on tensor products of composition algebras and on the Smirnov algebra

We give classifications of group gradings, up to equivalence and up to isomorphism, on the tensor product of a Cayley algebra $\mathcal{C}$ and a Hurwitz algebra over a field of characteristic different from 2. We also prove that the automorphism group schemes of $\mathcal{C}^{\otimes n}$ and $\mathcal{C}^n$ are isomorphic. On the other hand, we prove that the automorphism group schemes of a Smirnov algebra (a $35$-dimensional simple exceptional structurable algebra constructed from a Cayley algebra $\mathcal{C}$) and $\mathcal{C}$ are isomorphic. This is used to obtain classifications, up to equivalence and up to isomorphism, of the group gradings on Smirnov algebras.

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arXiv2018

Gradings on semisimple algebras

The classification of gradings by abelian groups on finite direct sums of simple finite-dimensional nonassociative algebras over an algebraically closed field is reduced, by means of the use of loop algebras, to the corresponding problem for simple algebras. This requires a good definition of (free) products of group-gradings.

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