CLASSIFICATION OF LEAVITT PATH ALGEBRAS WITH TWO VERTICES

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dc.contributor.authorKanuni, Müge
dc.contributor.authorBarquero, Dolores Martin
dc.contributor.authorGonzalez, Candido Martin
dc.contributor.authorMolina, Mercedes Siles
dc.date.accessioned2020-04-30T22:40:49Z
dc.date.available2020-04-30T22:40:49Z
dc.date.issued2019
dc.departmentDÜ, Fen-Edebiyat Fakültesi, Matematik Bölümüen_US
dc.descriptionKanuni, Muge/0000-0001-7436-039Xen_US
dc.descriptionWOS: 000476630800004en_US
dc.description.abstractWe 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 K-0 group, det(N-E') (included in the Franks invariants), the type, as well as the socle, the ideal generated by the vertices in cycles with no exits and the ideal generated by vertices in extreme cycles. The starting point is a simple linear algebraic result that determines when a Leavitt path algebra is IBN. An interesting result that we have found is that the ideal generated by extreme cycles is invariant under any isomorphism (for Leavitt path algebras whose associated graph is finite). We also give a more specific proof of the fact that the shift move produces an isomorphism when applied to any row-finite graph, independently of the field we are considering.en_US
dc.description.sponsorshipDuzce UniversityDuzce University [DUBAP-2016.05.04.462]; Junta de AndaluciaJunta de Andalucia [FQM-336, FQM-7156]; Fondos FEDEREuropean Union (EU) [FQM-336, FQM-7156, MTM2016-76327-C3-1-P]; Spanish Ministerio de Economia y Competitividad [MTM2016-76327-C3-1-P]en_US
dc.description.sponsorshipThe first named author is supported by Duzce University Bilimsel Arastirma Projesi titled "Leavitt, Cohn-Leavitt yol cebirlerinin ve C*-cizge cebirlerinin K-teorisi" with grant no: DUBAP-2016.05.04.462. The three remaining authors are supported by the Junta de Andalucia and Fondos FEDER, jointly, through projects FQM-336 and FQM-7156. They are also supported by the Spanish Ministerio de Economia y Competitividad and Fondos FEDER, jointly, through project MTM2016-76327-C3-1-P.en_US
dc.identifier.doi10.17323/1609-4514-2019-19-3-523-548en_US
dc.identifier.endpage548en_US
dc.identifier.issn1609-3321
dc.identifier.issn1609-4514
dc.identifier.issue3en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage523en_US
dc.identifier.urihttps://doi.org/10.17323/1609-4514-2019-19-3-523-548
dc.identifier.urihttps://hdl.handle.net/20.500.12684/3064
dc.identifier.volume19en_US
dc.identifier.wosWOS:000476630800004en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherIndependent Univ Moscow-Iumen_US
dc.relation.ispartofMoscow Mathematical Journalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLeavitt path algebraen_US
dc.subjectIBN propertyen_US
dc.subjecttypeen_US
dc.subjectsocleen_US
dc.subjectextreme cycleen_US
dc.subjectK-0en_US
dc.titleCLASSIFICATION OF LEAVITT PATH ALGEBRAS WITH TWO VERTICESen_US
dc.typeArticleen_US

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