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Adrián Rodrigo-Escudero

Publications and source records attributed to Adrián Rodrigo-Escudero.

7 recordsLinked to original sources
arXiv2021

Gradings on associative algebras with involution and real forms of classical simple Lie algebras

We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a finite-dimensional algebra can be obtained from them via a group homomorphism (although not in a unique way). We classify up to equivalence the fine gradings on simple associative algebras with involution over the field of real numbers (or any real closed field) and, as a consequence, on the real forms of classical simple Lie algebras.

math.RA↗
arXiv2020

Fine gradings and automorphism groups on associative algebras

First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an associative algebra such that the algebra is graded-simple and satisfies the DCC on graded left ideals. We give necessary and sufficient conditions for the grading to be fine. Then we assume that one of these necessary conditions to be fine is satisfied, and we compute the automorphism groups of the grading; the results are expressed in terms of the automorphism groups of a graded-division algebra. Finally we compute the automorphism groups of graded-division algebras in the case in which the ground field is the field of real numbers, and the underlying algebra (disregarding the grading) is simple and of finite dimension.

math.RA↗
arXiv2018

Gradings on simple real Lie algebras

English: This work is a doctoral thesis in mathematics by compendium of four articles. Here we explain, using a language as simple as possible, the results achieved in those articles. The general objective is the classification of gradings on simple real Lie algebras. The text is written in both english and spanish. ----- Español: Esta obra es una tesis doctoral en matemáticas por compendio de cuatro artículos. Aquí explicamos, utilizando un lenguaje lo más sencillo posible, los resultados alcanzados en esos artículos. El objetivo general es la clasificación de las graduaciones en las álgebras de Lie reales simples. El texto está escrito tanto en inglés como en español.

math.RT↗
arXiv2018

Clifford algebras as twisted group algebras and the Arf invariant

Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real Clifford algebras in terms of the Arf invariant of the associated quadratic forms over the field of two elements, and give new proofs of some classical results.

math.RA↗
arXiv2015

Classification of division gradings on finite-dimensional simple real algebras

We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give the classification, up to isomorphism, of (not necessarily division) gradings on such algebras. Linear algebra over the field of two elements plays an interesting role in the proofs.

math.RA↗