arXiv subjects

Fernando Montaner

Publications and source records attributed to Fernando Montaner.

4 recordsLinked to original sources

arXiv2023

Jordan 3-graded Lie algebras with polynomial identities

We study Jordan 3-graded Lie algebras satisfying 3-graded polynomial identities. Taking advantage of the Tits-Kantor-Koecher construction, we interpret the PI condition in terms of their associated Jordan pairs, which allows us to formulate an analogous of Posner-Rowen Theorem for strongly prime PI Jordan 3-graded Lie algebras. Arbitrary PI Jordan 3-graded Lie algebras are also described by introducing the Kostrikin radical of the Lie algebras.

math.RA↗

arXiv2022

Continuous Evolution Algebras

We formulate the notion of continuous evolution algebra in terms of differentiable matrix-valued functions, to then study those such algebras arising as solutions of ODE problems. Given their dependence on natural bases, matrix Lie groups provide a suitable framework where considering time-variant evolution algebras. We conclude by broadening our approach by considering continuous evolution algebras stemming as flow lines on matrix Lie groups.

math.RA↗

arXiv2020

The ideal of Lesieur-Croisot elements of Jordan pairs

We study the sets of elements of Jordan pairs whose local Jordan algebras are Lesieur-Croisot algebras, that is, classical orders in nondegenerate Jordan algebras with finite capacity. It is then proved that, if the Jordan pair is nondegenerate, the set of its Lesieur-Croisot elements is an ideal of the Jordan pair.

math.RA↗

arXiv2020

On von Neumann regularity of algebras of quotients of Jordan algebras

We address a Jordan version of Johnson theorem on (associative) algebras of quotients, namely whether a strongly nonsingular (the Jordan version of nonsingularity) has a von Neumann regular algebra of quotients. Although the answer is negative in general, we prove that the result holds in the important case of algebras satisfying a polynomial identity.

math.RA↗