Extreme cycles : the center of a Leavitt path algebra
Corrales García, María G. (Universidad de Panamá. Centro Regional Universitario de Coclé: "Dr. Bernardo Lombardo")
Martín Barquero, Dolores (Universidad de Málaga. Escuela Técnica Superior de Ingenieros Industriales)
Martín González, Cándido (Universidad de Málaga. Departamento de Álgebra, Geometría y Topología)
Siles Molina, Mercedes (Universidad de Málaga. Departamento de Álgebra, Geometría y Topología)
Solanilla Hernández, José F. (Universidad de Panamá. Centro Regional Universitario de Coclé: "Dr. Bernardo Lombardo")

Data:	2016
Resum:	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 [13]. We will go further into the structure itself of the Leavitt path algebra. For example, the ideal I(Pec ∪ Pc ∪ Pl) generated by vertices in extreme cycles (Pec), by vertices in cycles without exits (Pc), and by line points (Pl) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to Pl ∪ Pc ∪ Pec. 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 (Pb∞).
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Leavitt path algebra ; Center ; Socle ; Extreme cycle ; Cycle ; Line point
Publicat a:	Publicacions matemàtiques, Vol. 60 Núm. 1 (2016) , p. 235-263 (Survey) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/302249
DOI: 10.5565/PUBLMAT_60116_09

29 p, 461.1 KB

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