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Manuel Ladra

Publications and source records attributed to Manuel Ladra.

At least 19 recordsLinked to original sources
arXiv2026

Representations of compatible Lie algebras

We study compatible Lie algebras from algebraic and representation-theoretic points of view, obtaining counterexamples to some fundamental theorems from classical Lie algebra theory, namely the theorems of Lie, Weyl and Levi. We also classify the two-dimensional compatible Lie algebras up to isomorphism and explore their representation theory, presenting families of indecomposable non-semisimple representations, showing that the solvable two-dimensional compatible Lie algebras have wild representation type, and classifying all irreducible finite-dimensional line representations. Finally, we prove a Clebsch-Gordan decomposition for tensor products of finite-dimensional irreducible line representations.

math.RT↗
arXiv2026

Further results on modularity in evolution algebras

In this paper, we study modularity in the context of evolution algebras. Although this property has been previously considered, a complete description is still missing in several natural settings. In particular, we obtain a full characterisation of modular evolution algebras in the nilpotent case and in the class of supersolvable regular evolution algebras.

math.RA↗
arXiv2026

On a family of non-Volterra quadratic operators acting on a simplex

In the present paper, we consider a convex combination of non-Volterra quadratic stochastic operators defined on a finite-dimensional simplex depending on a parameter $\alpha$ and study their trajectory behaviors. We showed that for any $\alpha\in [0,1)$ the trajectories of such operator converge to a fixed point. For $\alpha=1$ any trajectory of the operator converges to a periodic trajectory.

math.DS↗
arXiv2026

HNN-extension of Lie superalgebras

We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a two-generator Lie superalgebra.

math.RA↗
arXiv2026

Notes on Leibniz $n$-algebras

We analyze behaviors of generalized forgetful and Daletskii-Takhtajan's functors on perfect objects and crossed modules of Leibniz $n$-algebras. Then we give applications to homology and universal central extensions of Leibniz $n$-algebras.

math.RA↗
arXiv2025

A Frattini theory for evolution algebras

This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic evolution algebras.

math.RA↗
arXiv2025

Regular evolution algebras are closed under subalgebras

The main goal of this note is to show that subalgebras of regular evolution algebras are themselves evolution algebras. This allows us to assume, without loss of generality, that every subalgebra in the regular setting has a basis consisting of vectors with disjoint supports. Finally, we use this result to characterise the existence of codimension-one subalgebras in regular evolution algebras.

math.RA↗
arXiv2025

On the subalgebra lattice of solvable evolution algebras

The main objective of this paper is to study the relationship between a solvable evolution algebra and its subalgebra lattice, emphasizing two of its main properties: distributivity and modularity. First, we will focus on the nilpotent case, where distributivity is characterised, and a necessary condition for modularity is deduced. Subsequently, we comment on some results for solvable non-nilpotent evolution algebras, finding that the ones with maximum index of solvability have the best properties. Finally, we characterise modularity in this particular case by introducing supersolvable evolution algebras and computing the terms of the derived series.

math.RA↗
arXiv2024

A non-abelian tensor product of algebras with bracket

We introduce and study a non-abelian tensor product of two algebras with bracket with compatible actions on each other. We investigate its applications to the universal central extensions and the low-dimensional homology of perfect algebras with bracket.

math.RA↗
arXiv2024

A classification of nilpotent compatible Lie algebras

Working over an arbitrary field of characteristic different from $2$, we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent compatible Lie algebras up to dimension $4$. In case the base field is cubically closed, we find that there are three isomorphism classes and a one-parameter family in dimension $3$, and $12$ isomorphism classes, $6$ one-parameter families and two $2$-parameter families in dimension $4$

math.RA↗
arXiv2023

Wells type exact sequence and crossed extensions of algebras with bracket

We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second cohomology. Finally, we construct an eight term exact sequence in the cohomology of algebras with bracket.

math.KT↗
arXiv2023

$q$-crossed modules and $q$-capability of Lie algebras

Given a non-negative integer $q$, we study two different notions of the $q$-capability of Lie algebras via the non-abelian $q$-exterior product of Lie algebras. The first is related to the $q$-crossed modules and inner $q$-derivations, and the second is the Lie algebra version of the $q$-capability of groups proposed by Ellis in 1995.

math.RA↗
arXiv2019

Universal central extensions of braided crossed modules in Lie algebras

In this paper, we give a natural braiding on the universal central extension of a crossed module of Lie algebras with a given braiding and construct the universal central extension of a braided crossed module of Lie algebras, showing that, when one of the constructions exists, both exist and coincide.

math.RA↗