Listar por autor "Gil-Canto, Cristóbal"
Mostrando ítems 1-13 de 13
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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 ... -
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 ... -
Largest ideals in Leavitt path algebras.
Cam, Vural; Gil-Canto, Cristóbal; Kanuni, Müge; Siles-Molina, Mercedes (Springer Nature, 2020-02-22)
We identify largest ideals in Leavitt path algebras: the largest locally left/right artinian (which is the largest semisimple one), the largest locally left/right noetherian without minimal idempotents, the largest exchange, ... -
Leavitt path algebras of Cayley graphs C_n^j.
Abrams, Gene; Erickson, Stefan; Gil-Canto, Cristóbal (Springer Nature, 2018-09-15)
Let n be a positive integer. For each 0 <= j <= n-1 we let C_n^j denote the Cayley graph of the cyclic group Zn with respect to the subset {1,j}. Utilizing the Smith Normal Form process, we give an explicit description of ... -
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 the structure of Leavitt path algebras and Kumjian-Pask algebras.
Gil-Canto, Cristóbal (UMA Editorial, 2017-01-15)
Esta tesis doctoral pretende continuar y avanzar en el conocimiento de las álgebras de caminos de Leavitt. Para un grafo dirigido E, el álgebra de caminos de Leavitt L(E) es el análogo algebraico de la C*-álgebra de ... -
Representations of relative Cohn path algebras.
Gil-Canto, Cristóbal; Gonçalves, Daniel (Elsevier, 2020-01-07)
We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings. To do this we prove uniqueness theorems for relative Cohn path algebras. Furthermore, given ... -
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 ... -
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 ... -
The commutative core of a Leavitt path algebra.
Gil-Canto, Cristóbal; Nasr-Isfahani, Alireza (Elsevier, 2018-06-30)
For any unital commutative ring R and for any graph E, we identify the commutative core of the Leavitt path algebra of E with coefficients in R, which is a maximal commutative subalgebra of the Leavitt path algebra. ... -
The cycline subalgebra of a Kumjian-Pask algebra.
Clark, Lisa Orloff; Gil-Canto, Cristóbal; Nasr-Isfahani, Alireza (American Mathematical Society, 2016-11-21)
Let $\Lambda$ be a row-finite higher-rank graph with no sources. We identify a maximal commutative subalgebra $\mathcal{M}$ inside the Kumjian-Pask algebra ${\rm KP}_R(\Lambda)$. We also prove a generalized Cuntz-Krieger ... -
The reduction theorem for algebras of one-sided subshifts over arbitrary alphabets.
Bagio, Dirceu; Gil-Canto, Cristóbal; Gonçalves, Daniel; Royer, Danilo (Springer, 2024-02-21)
Let R be a commutative unital ring, X a subshift, and A_R(X) the corresponding unital subshift algebra. We establish the reduction theorem for A_R(X). As a consequence, we obtain a Cuntz-Krieger uniqueness theorem for ...