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The socle of a Leavitt path algebra
- Source :
-
Journal of Pure & Applied Algebra . Mar2008, Vol. 212 Issue 3, p500-509. 10p. - Publication Year :
- 2008
-
Abstract
- Abstract: In this paper we characterize the minimal left ideals of a Leavitt path algebra as those which are isomorphic to principal left ideals generated by line points; that is, by vertices whose trees 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 certain algebras that arise as the Leavitt path algebra of a row-finite graph. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra. [Copyright &y& Elsevier]
- Subjects :
- *ALGEBRA
*ISOMORPHISM (Mathematics)
*GRAPH theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 212
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 27627304
- Full Text :
- https://doi.org/10.1016/j.jpaa.2007.06.001