arXiv subjects

Germán Benitez

Publications and source records attributed to Germán Benitez.

5 recordsLinked to original sources

arXiv2026

Cochain complexes over an endofunctor

We introduce the categories of left and right complexes for (additive) endofunctors over an additive category $\mathcal{C}$. These categories unify the definitions of complexes over an additive category and modules over repetitive algebras. Supported by Eilenberg-Moore theory and Happel's successful work, we study the descriptions and properties of these categories, highlighting both similarities and differences with complexes and modules over repetitive algebras. We also examine the influence and interaction of these categories with the category of endofunctors, leading to applications in the representation theory of algebras and with eventual applications in ($2$-)algebraic geometry.

math.RT↗

arXiv2026

Lie 2-algebras of toral rank 3

In this paper we study Lie 2-algebras over an algebraically closed field of characteristic two, which have a triangulable Cartan subalgebra, and derive some general properties of centerless ones. These properties allow us to do an analysis on simple Lie 2-algebras of toral rank three and provide a necessary condition for simplicity. By means of this latter condition we also conclude that simple Lie 2-algebras with a triangulable Cartan subalgebra of toral rank three and of dimension less than or equal to 16 cannot exist.

math.RA↗

arXiv2025

From the homotopy category of projective modules over gentle algebras to poset representations

In [BCP24], the authors describe a triangulated structure of a quotient of a certain category of representations of posets, nowadays known as the Bondarenko's category. This category was essential in [BM03] for classify all indecomposable objects of the derived category of gentle algebras. In view of this connection with the derived category, which possess a triangulated structure. In this paper, we identify another triangulated structure for Bondarenko's category, allowing us to utilize the functor presented in [BM03]. This functor will establishes a connection between the triangulated structure of the homotopy category of gentle algebras and the new triangulated structure of a quotient of a certain Bondarenko's category.

math.RT↗

arXiv2024

Triangulated structure for Bondarenko's Categories

V. Bondarenko and Y. Drozd gives a description of all indecomposable objects in a category of representations of posets, nowadays known as the Bondarenko's category. This category was essential for V. Bekkert and H. Merklen classify all indecomposable objects of the derived category of gentle algebras. In view of this connection with the derived category, which possess a triangulated structure, and of the fact that in this paper we show that the Bondarenko's category is not an abelian category, it is reasonable to contemplate the existence of a triangulated structure for the Bondarenko's category. In this paper we introduce a triangulated category structure over a quotient of Bondarenko's category, which will allow to use the techniques of triangulated category to study representations of posets.

math.RT↗

arXiv2021

Faces of polyhedra associated with relation modules

Relation Gelfand-Tsetlin $\mathfrak{gl}_n$-modules were introduced in [FRZ19], and are determined by some special directed graphs and Gelfand-Tsetlin characters. In this work we constructed polyhedra associated with the class of relation modules, which includes as a particular case, any classical Gelfand-Tsetlin polytope. Following the ideas presented in [LM04] we give a characterization of $d$-faces of the associated polyhedra in terms of a matrix related to the corresponding graph.

math.RT↗