Álgebra, Geometría y Topología - (AGT)
Estas son las colecciones en las que puede catalogar la producción investigadora del departamento Álgebra, Geometría y Topología. Si considera que ninguna de estas se ajusta a su material pida una nueva colección en la sección de sugerencias.
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Quiver representations for Leavitt Path algebras as talented monoid classification detour.
(2024)There is a correspondence between quiver representations and path algebras. In this talk, we will see Leavitt Path algebras as a special case for such representation and how it will take a role in its classifications in ... -
Spectrum of the Laplacian on homogeneous spaces.
(2024)We will start with an introduction and stating general results on the spectral properties of the Laplacian before we investigate the restriction to manifolds which are symmetric. We consider the difference of spectral ... -
On isomorphism conditions for algebra functors with applications to Leavitt Path Algebras
(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 ... -
Tensor product of evolution algebras.
(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 ... -
Two-dimensional perfect evolution algebras over domains
(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 ... -
Ternary mappings of triangular algebras
(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. -
Classification of leavitt path algebras with two vertices
(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 ... -
Using the Steinberg Algebra Model to determine the center of any Leavitt Path Algebra
(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 ... -
Squares and associative representations of two dimensional evolution algebras
(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 ... -
g2 como anillo grupo torcido
(2024)El objetivo es presentar la construcción del álgebra de Lie compacta excepcional g2 como un anillo grupo torcido para el grupo Z2-cubo y el anillo suma de dos copias de los números reales. El modelo es autocontenido, ... -
Conjugacy of subshifts via the associated algebras.
(2024)In this talk, we present the recently defined unital algebra associated with a one-sided subshift over an arbitrary alphabet. For finite alphabets, the C*-algebraic version of this algebra coincides with the C*-algebra ... -
Entropy of local homeomorphisms with applications to subshifts arising from infinite graphs.
(2024)In this talk, we introduce topological entropy for dynamical systems generated by a single local homeomorphism (Deaconu-Renault systems). More precisely, we propose and compare entropy definitions via covers and via separated ... -
The Exceptional Lie algebra G_2.
(2023)The Killing-Cartan classification of finite-dimensional complex simple Lie algebras was one of the great milestones of 19th-century mathematics. According to it, there are four infinite families of classical simple Lie ... -
Invariant ideals in Leavitt path algebras.
(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 ... -
Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence.
(Elsevier, 2023-07-10)For n ≥ 2 and fixed k ≥ 1, we study when an endomorphism f of Fn, where F is an arbitrary field, can be decomposed as t + m where t is a root of the unity endomorphism and m is a nilpotent endomorphism with mk = 0. For ... -
Gradings induced by nilpotent elements.
(Elsevier, 2023)An element a is nilpotent last-regular if it is nilpotent and its last nonzero power is von Neumann regular. In this paper we show that any nilpotent last-regular element a in an associative algebra R over a ring of scalars ... -
A filtration associated to an abelian inner ideal of a Lie algebra.
(Elsevier, 2022-12-14)Let B be an abelian inner ideal and let KerL B be the kernel of B. In this paper we show that when there exists n ∈ N with [B,KerL B] n ⊂ B, the inner ideal B induces a bounded filtration in L where B is the first nonzero ... -
Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence.
(International Linear Algebra Society, 2023-08-24)For any n ≥ 2 and fixed k ≥ 1, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring Mn(F) to be written as a sum of an invertible matrix U and a nilpotent matrix N with Nk ... -
Context-Equivalence of Algebras with Involutions.
(2023)Morita equivalence is the central concept of celebrated Morita theory. Two algebras are Morita equivalent if their categories of modules are equivalent. A Morita context is a useful technical concept that allows one to ... -
Introducción a la fiabilidad algebraica.
(2023)La teoría de fiabilidad se encarga de analizar la disponibilidad y fiabilidad de procesos y sistemas industriales, redes, etc. Existen muchos métodos para el cálculo de fiabilidad de sistemas, es un área en continuo ...