RT Journal Article
T1 Classification of leavitt path algebras with two vertices
A1 Kanuni, Müge
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
A1 Siles-Molina, Mercedes
K1 Álgebra
AB We 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 K0 group, detpNE1 q (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 isomorphismwhen applied to any row-finite graph, independently of the field we are considering.
PB Independent University of Moscow
YR 2019
FD 2019-07
LK https://hdl.handle.net/10630/29728
UL https://hdl.handle.net/10630/29728
LA eng
NO Kanuni M., Martín Barquero, D., Martín González, D, and Siles Molina, M. Classification of Leavitt Path Algebras with Two Vertices. Mosc. Math. J. 19 (2019), no. 3, 523–548.
NO Düzce University Bilimsel Ara ̧stırma Projesi titled “Leavitt, Cohn- Leavitt yol cebirlerinin ve C*-cizge cebirlerinin K-teorisi” with grant no: DUBAP-2016.05.04.462. Junta de Andalucía and Fondos FEDER, jointly, projects FQM- 336 and FQM-7156. Spanish Ministerio de Economía y Competitividad and Fondos FEDER,  project MTM2016-76327-C3-1-P.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026