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Listar por autor "Martin-Gonzalez, Candido"
Mostrando ítems 1-19 de 19
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Algebraic entropy of path algebras and Leavitt path algebras of finite graphs.
Bock, Wolfgang; Gil-Canto, Cristóbal
; Martín-Barquero, Dolores; Martín-González, Cándido; Ruiz Campos, Iván; Sebandal, Alfilgen[et al.] (Springer Nature, 2024)
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 algebras. For the path algebras, Leavitt ... -
Chains in evolution algebras
Cabrera-Casado, Yolanda; Cardoso Gonçalves, Maria Inez; Gonçalves, Daniel; Martín-Barquero, Dolores; Martín-González, Cándido (ELSEVIER, 2021-08-01)
In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, we provide four different constructions producing three-dimensional evolution ... -
Classification of leavitt path algebras with two vertices
Kanuni, Müge; Martín-Barquero, Dolores; Martín-González, Cándido; Siles-Molina, Mercedes (Independent University of Moscow, 2019-07)
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 K0 group, detpNE1 q (included in the Franks ... -
Commutative algebras with one-dimensional square
Martín-Barquero, Dolores; Martín-González, Cándido; Sánchez-Ortega, Juana (Springer Nature, 2025-02-26)
In this paper, we classify and study commutative algebras having a one-dimensional square. In finite dimension (see Theorem 3.9) besides some cases (which are all associative and nilpotent with nilpotency index 3), the ... -
Connecting ideals in evolution algebras with hereditary subsets of its associated graph
Cabrera-Casado, Yolanda; Martín-Barquero, Dolores; Martín-González, Cándido; Tocino-Sánchez, Alicia (2023)
In this article, we introduce a relation including ideals of an evo-lution algebra and hereditary subsets of vertices of its associated graph andestablish some properties among them. This relation allows us to determinemaximal ... -
Invariant ideals in Leavitt path algebras.
Gil-Canto, Cristóbal; Martín-Barquero, Dolores; Martín-González, Cándido (Universitat Autònoma de Barcelona, Departament de Matemàtiques. Revista: Publications Matematiques, 2020-06-23)
It is known that the ideals of a Leavitt path algebra LK (E) generated by Pl(E), by Pc(E) or by Pec(E) are invariant under isomorphism. Though the ideal generated by Pb∞ (E) is not invariant we find its “natural” replacement ... -
On isomorphism conditions for algebra functors with applications to Leavitt Path Algebras
Gil-Canto, Cristóbal; Martín-Barquero, Dolores; Martín-González, Cándido; Ruiz Campos, Iván (SpringerLink, 2023-07)
We introduce certain functors from the category of commu- tative rings (and related categories) to that of Z-algebras (not neces- sarily associative or commutative). One of the motivating examples is the Leavitt path ... -
On simple evolution algebras of dimension two and three. Constructing simple and semisimple evolution algebras.
Cabrera-Casado, Yolanda; Martín-Barquero, Dolores; Martín-González, Cándido; Tocino-Sánchez, Alicia (Taylor & Francis, 2024-05-13)
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, inductive limit group, Zariski topology and the ... -
Sigma-maps on triangular algebras
Sánchez-Ortega, Juana; Repka, Joe; Martín-González, Cándido (2018-01-30)
Triangular algebras were introduced by Chase in the early 1960s. He ended up with these structures in the course of his study of the asymmetric behavior of semi-hereditary rings. Since their introduction, triangular ... -
Simultaneous orthogonalization of inner products in infinite-dimensional vector spaces
Cabrera-Casado, Yolanda; Gil-Canto, Cristóbal; Martín-Barquero, Dolores; Martín-González, Cándido (Taylor and Francis, 2025)
For an arbitrary field K and a family of inner products in a K-vector space V of arbitrary dimension, we study necessary and sufficient conditions in order to have a basis which is orthogonal relative to all the inner ... -
Simultaneous orthogonalization of inner products over arbitrary fields.
Cabrera-Casado, Yolanda; Gil-Canto, Cristóbal; Martín-Barquero, Dolores; Martín-González, Cándido (Springer, 2023)
We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space V over an arbitrary field K to have an orthogonal basis relative to all the inner products. Some applications ... -
Squares and associative representations of two dimensional evolution algebras
Cardoso Gonçalves, Maria Inez; Gonçalves, Daniel; Martín-Barquero, Dolores; Martín-González, Cándido; Siles-Molina, Mercedes (World Scientific, 2021)
We associate an square to any two dimensional evolution algebra. This geomet- ric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the ... -
Tensor Product of Evolution Algebras
Cabrera-Casado, Yolanda; Martín-Barquero, Dolores; Martín-González, Cándido; Tocino-Sánchez, Alicia (Springer Nature, 2022-12-28)
The starting point of this work is the fact that the class of evolution algebras over a fixed field is closed under tensor product. We prove that, under certain conditions, the tensor product is an evolution algebra if and ... -
Tensor product of evolution algebras.
Cabrera-Casado, Yolanda; Martín-Barquero, Dolores; Martín-González, Cándido; Tocino-Sánchez, Alicia (SpringerLink, 2022-12-28)
The starting point of this work is the fact that the class of evolution algebras over a fixed field is closed under tensor product. We prove that, under certain conditions, the tensor product is an evolution algebra if and ... -
Ternary mappings of triangular algebras
Martín-Barquero, Dolores; Martín-González, Cándido; Sánchez-Ortega, Juana; Vandeyar, Morgan (SpringerLink, Aequationes Mathematicae, 2021-03)
We take acategorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied. -
The algebraic entropies of the Leavitt path algebra and the graph algebra agree.
Martín-Barquero, Dolores; Bock, Wolfgang; Ruiz Campos, Iván; Gil-Canto, Cristóbal; Martín-González, Cándido; Sebandal, Alfilgen[et al.] (Springer Nature, 2024-10-24)
In this note we prove that the algebras L_K(E) and KE have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The main argument leans on (1) the holomorphic ... -
Two-dimensional perfect evolution algebras over domains
Cabrera-Casado, Yolanda; Martín-Barquero, Dolores; Martín-González, Cándido (SpringerLink, 2023-01)
We will study evolution algebras A that are free modules of dimension two over domains. We start by making some general considerations about algebras over domains: They are sandwiched between a certain essential D-submodule ... -
Two-dimensional perfect evolution algebras over domains.
Cabrera-Casado, Yolanda; Martín-Barquero, Dolores; Martín-González, Cándido (Springer Nature, 2023-01-23)
We will study evolution algebras A that are free modules of dimension two over domains. We start by making some general considerations about algebras over domains: They are sandwiched between a certain essential D-submodule ... -
Using the Steinberg Algebra Model to determine the center of any Leavitt Path Algebra
Clark, Lisa Orloff; Martín-Barquero, Dolores; Martín-González, Cándido; Siles-Molina, Mercedes (Springer, 2019-04)
Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization ...