Weakly Regular and Self-Injective Leavitt Path Algebras Over Arbitrary Graphs

Pino, Gonzalo Aranda; Rangaswamy, Kulumani M.; Molina, Mercedes Siles

doi:10.1007/s10468-010-9215-9

Cited by 17 publications

(1 citation statement)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The ideal generated by P l (E), isomorphic to a direct sum of matrix rings over K, is precisely the socle of the Leavitt path algebra (this was studied in [9,10,12]), so it contains the locally artinian side of the Leavitt path algebra. On the other hand, P c (E) contains the information about the locally noetherian character of the Leavitt path algebra: the ideal generated by P c (E) is isomorphic to a direct sum of matrix rings over K[x, x −1 ]; this was determined in [3,7].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Extreme cycles. The center of a Leavitt path algebra

García¹,

Barquero²,

González³

et al. 2016

Publicacions Matemàtiques

View full text Add to dashboard Cite

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 ∪ P l) generated by vertices in extreme cycles (Pec), by vertices in cycles without exits (Pc), 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 ∪ 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 (P b ∞).

show abstract