1 citations · 2 across the 12 of their papers we have counts for
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Algebraic entropy and a complete classification of path algebras over finite graphs by growth
Wolfgang Bock, Cristóbal Gil Canto, Dolores Martín Barquero +3
The Gelfand-Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path a…
Central extensions of axial algebras
Ivan Kaygorodov, Cándido Martín González, Pilar Páez-Guillán
In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial centra…
On simple evolution algebras of dimension two and three. Constructing simple and semisimple evolution algebras
Yolanda Cabrera Casado, Dolores Martín Barquero, Cándido Martín González +1
This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, induct…
Two dimensional perfect evolution algebras over domains
Yolanda Cabrera Casado, Dolores Martín Barquero, Cándido Martín González
We will study evolution algebras which are free modules of dimension over domains. Furthermore, we will assume that these algebras are perfect, that is . We start by…
Evolution algebras with one-dimensional square
Chad Brache, Dolores Martín Barquero, Cándido Martín González +1
Evolution algebras with one dimensional square are classified using the theory of inner product spaces. More precisely, for an evolution algebra with and a…
Simultaneous orthogonalization of inner products over arbitrary fields
Yolanda Cabrera Casado, Cristóbal Gil Canto, Dolores Martín Barquero +1
We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space over an arbitrary field to have an orthogonal basis…
Invariants ideals in Leavitt Path algebras
Cristóbal Gil Canto, Dolores Martín Barquero, Cándido Martín González
It is known that the ideals of a Leavitt path algebra generated by $\Pl(E)$, by $\Pc(E)$ or by $\Pec(E)$ are invariant under isomorphism. Though the ideal generated by $\P…
On the centroid of a Leavitt path algebra
Daniel Gonçalves, Dolores Martín Barquero, Cándido Martín González +1
We describe the centroid of some Leavitt path algebras. More precisely, we show that for Leavitt path algebras over a field that are simple its centroid is isomorphic to , a…
Squares and associative representations of two dimensional evolution algebras
Maria Inez Cardoso Gonçalves, Daniel Gonçalves, Dolores Martín Barquero +2
We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the beha…
Classification of Leavitt path algebras with two vertices
Müge Kanuni, Dolores Martín Barquero, Cándido Martín González +1
We classify row-finite Leavitt path algebras associated to graphs with no more than two vertices. For the discussion we use the following invariants: decomposability, the gro…
On the gauge action of a Leavitt path algebra
María Guadalupe Corrales García, Dolores Martín Barquero, Cándido Martín González
We introduce a revised notion of gauge action in relation with Leavitt path algebras. This notion is based on group schemes and captures the full information of the grading on the…
Centers of path algebras, Cohn and Leavitt path algebras
María Guadalupe Corrales García, Dolores Martín Barquero, Cándido Martín González +2
We study the center of several types of path algebras. We start with the path algebra and prove that if the number of vertices is infinite then the center is zero. Otherwise,…
Atlas of Leavitt Path Algebras of small graphs
Pablo Alberca Bjerregaard, Gonzalo Aranda Pino, Dolores Martín Barquero +2
The aim of this work is the description of the isomorphism classes of all Leavitt path algebras coming from graphs satisfying Condition (Sing) with up to three vertices. In particu…