Papers by Candido martin gonzalez
Non Associative Graded Algebras
Non-Associative Algebra and Its Applications, 1994
Journal of the Mathematical Society of Japan, 2014
The aim of this work is the description of the isomorphism classes of all Leavitt path algebras c... more 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 particular, this classification recovers the one achieved by Abrams et al. in the case of graphs whose Leavitt path algebras are purely infinite simple. The description of the isomorphism classes is given in terms of a series of invariants including the K 0 group, the socle, the number of loops with no exits and the number of hereditary and saturated subsets of the graph.
This paper is devoted to the study of the center of several types of path algebras associated to ... more This paper is devoted to the study of the center of several types of path algebras associated to a graph E over a field K. In a first step we consider the path algebra KE and prove that if the number of vertices is infinite then the center is zero; otherwise, it is K, except when the graph E is a cycle in which case the center is K[x], the polynomial algebra in one indeterminate. Then we compute the centers of prime Cohn and Leavitt path algebras. A lower and an upper bound for the center of a Leavitt path algebra are given by introducing the graded Baer radical for graded algebras.
Journal of Pure and Applied Algebra, 2008
In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones whi... more In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones which are isomorphic to principal left ideals generated by line point vertices, that is, by vertices whose trees do not contain neither bifurcations nor closed paths. Moreover, we show that the socle of a Leavitt path algebra is the two-sided ideal generated by these line point vertices. This characterization allows us to compute the socle of some algebras that arise as the Leavitt path algebra of some row-finite graphs. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra.
Revista Matemática Iberoamericana, 2000
The main aim of the paper is to give a socle theory for Leavitt path algebras of arbitrary graphs... more The main aim of the paper is to give a socle theory for Leavitt path algebras of arbitrary graphs. We use both the desingularization process and combinatorial methods to study Morita invariant properties concerning the socle and to characterize it, respectively. Leavitt path algebras with nonzero socle are described as those which have line points, and it is shown that the line points generate the socle of a Leavitt path algebra, extending so the results for row-finite graphs in the previous paper (but with different methods). A concrete description of the socle of a Leavitt path algebra is obtained: it is a direct sum of matrix rings (of finite or infinite size) over the base field.
Compact graph C ∗-algebras
Revista Matemática Complutense, 2013
ABSTRACT Compactness of graph C * -algebras C * (E), for arbitrary directed graphs E, is characte... more ABSTRACT Compactness of graph C * -algebras C * (E), for arbitrary directed graphs E, is characterized structurally and graph-theoretically. In the first direction, C * (E) is proved to be compact if and only if it is isomorphic to a C * -direct sum of subalgebras isomorphic to either finite matrix algebras over ℂ or the algebra of compact operators on a separable complex Hilbert space. The graph-theoretic characterization is that C * (E) is compact if and only if E is acyclic and row-finite (each vertex emits at most finitely many arrows) and every infinite (forward) path in E ends in an infinite sink (an infinite path none of whose vertices hosts a bifurcation or a cycle). These are exactly the conditions under which any Leavitt path algebra L K (E) is semisimple in the sense of being equal to its socle. Other results include a description of the socle of C * (E) in general, and characterizations of the simple compact graph C * -algebras.
Journal of Pure and Applied Algebra, 2008
In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones whi... more In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones which are isomorphic to principal left ideals generated by line point vertices, that is, by vertices whose trees do not contain neither bifurcations nor closed paths. Moreover, we show that the socle of a Leavitt path algebra is the two-sided ideal generated by these line point vertices. This characterization allows us to compute the socle of some algebras that arise as the Leavitt path algebra of some row-finite graphs. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra.
In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path... more In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line points and vertices in cycles without exits, are the key ingredients in order to determine the center of a Leavitt path algebra. Our work will rely on our previous approach to the center of a prime Leavitt path algebra . We will go further into the structure itself of the Leavitt path algebra. For example, the ideal I(P ec ∪ P c ∪ P l ) generated by vertices in extreme cycles (P ec ), by vertices in cycles without exits (P c ) and by line points (P l ) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to P l ∪P c ∪P ec . Hence its structure will contain much of the information about the Leavitt path algebra. In the row-finite case, we will need to add a new hereditary set: the set of vertices whose tree has infinite bifurcations (P b ∞ ).
Nuevas aportaciones en h*-teorías
Characterization of rings using socle-fine and radical-fine notions
Ring Theory and Algebraic Geometry Proceedings of the Fifth International Conference in Leon Spain 2001 Isbn 0 8247 0559 9 Pags 211 221, 2001
Introducción algebráica a los calendarios Juliano y Gregoriano
Epsilon Revista De La Sociedad Andaluza De Educacion Matematica Thales, 1987
Compact graph C*-algebras
Revista Matematica Complutense, 2013
ABSTRACT Compactness of graph C * -algebras C * (E), for arbitrary directed graphs E, is characte... more ABSTRACT Compactness of graph C * -algebras C * (E), for arbitrary directed graphs E, is characterized structurally and graph-theoretically. In the first direction, C * (E) is proved to be compact if and only if it is isomorphic to a C * -direct sum of subalgebras isomorphic to either finite matrix algebras over ℂ or the algebra of compact operators on a separable complex Hilbert space. The graph-theoretic characterization is that C * (E) is compact if and only if E is acyclic and row-finite (each vertex emits at most finitely many arrows) and every infinite (forward) path in E ends in an infinite sink (an infinite path none of whose vertices hosts a bifurcation or a cycle). These are exactly the conditions under which any Leavitt path algebra L K (E) is semisimple in the sense of being equal to its socle. Other results include a description of the socle of C * (E) in general, and characterizations of the simple compact graph C * -algebras.
Computational approach to the simplicity of f4(Os,-) in the characteristic two case
Journal of Computational and Applied Mathematics, Sep 1, 2003
We present in this paper a computational approach to the study of the simplicity of the derivatio... more We present in this paper a computational approach to the study of the simplicity of the derivation Lie algebra of the quadratic Jordan algebra H3(Os,-), denoted by f4(Os,-), when the characteristic of the base field is two. We will show not only a collection of routines designed to find identities and construct principal ideals but also a philosophy of how to proceed studying the simplicity of a Lie algebra. We have first implemented the quadratic Jordan structure of H3(Os,-) into the computer system Mathematica (Computing the derivation Lie algebra of the quadratic Jordon Algebra H3(Os,-) at any characteristic, preprint, 2001) and then determined the generic expression of an element of the Lie algebra (see (41)). Once the structure of is completely described, it is time to analyze the simplicity by using the strategy mentioned. If the characteristic of the base field is not two, the Lie algebra is simple, but if the characteristic is two, the Lie algebra is not simple and there exists only one proper nonzero ideal I which is 26 dimensional and simple as a Lie algebra. In order to prove this last affirmation, we have used again the set of routines to show the simplicity of the ideal and that it is isomorphic to , which is also a simple Lie algebra. This isomorphism is constructed from a computed Cartan decomposition of both Lie algebras.
The Banach-Lie group of Lie automorphisms of an H-algebra
Bollettino Dell Unione Matematica Italiana Sezione B Articoli Di Ricerca Matematica, 2007
We introduce a revised notion of gauge action in relation with Leavitt path algebras. This notion... more 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 algebra as it is the case of the gauge action of the graph $C^*$-algebra of the graph.
Special jordan H-triple systems
Commun Algebra, 2000
Page 1. COMMUNICATIONS IN ALGEBRA, 28(10), 46994706 (2000) SPECIAL JORDAN H*-TRIPLE SYSTEMS. Albe... more Page 1. COMMUNICATIONS IN ALGEBRA, 28(10), 46994706 (2000) SPECIAL JORDAN H*-TRIPLE SYSTEMS. Alberto Castell6n Serrano Jose Antonio Cuenca Mira and CQndido Martin Gonzblez. Departamento de Algebra ...
The banach-lie group of lie triple automorphisms of an H*-algebra
Acta Math Sci, 2010
... not satisfy the standard No.4 Mart n & Gonz alez : BANACH-LIE GROUP OF LIE TRIPLE AUTOMOR... more ... not satisfy the standard No.4 Mart n & Gonz alez : BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS 1221 ... LH prime(H), hence in HS(H). So, the algebra HS(H) is an example of a prime algebra with ... In the context of nonzero socle, primeness is equivalent to primitiveness ...
Sobre el S-radical de un par asociativo y un teorema tipo Wedderburn para sistemas triples asociativos
Xiv Jornadas Hispano Lusas De Matematicas Vol 1 1989 Isbn 84 7756 240 7 Pags 39 44, 1989
Communications in Algebra, May 9, 2013
In this note we study associative dialgebras proving that the most interesting such structures ar... more In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection"property (simpleness, primitiveness, primeness or semiprimeness) imply that the dialgebra comes from an associative algebra with both products ⊣ and ⊢ identified. We also describe the class of zero-cubed algebras and apply its study to that of dialgebras. Finally we describe two-dimensional associative dialgebras.
Publicacions Matemàtiques, 2016
In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path... more In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line points and vertices in cycles without exits, are the key ingredients in order to determine the center of a Leavitt path algebra. Our work will rely on our previous approach to the center of a prime Leavitt path algebra . We will go further into the structure itself of the Leavitt path algebra. For example, the ideal I(P ec ∪ P c ∪ P l ) generated by vertices in extreme cycles (P ec ), by vertices in cycles without exits (P c ) and by line points (P l ) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to P l ∪P c ∪P ec . Hence its structure will contain much of the information about the Leavitt path algebra. In the row-finite case, we will need to add a new hereditary set: the set of vertices whose tree has infinite bifurcations (P b ∞ ).
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Papers by Candido martin gonzalez