RT info:eu-repo/semantics/article
T1 Cycles in Leavitt path algebras by means of idempotents
A1 Aranda Pino, Gonzalo
A1 Brox, Jose
A1 Siles Molina, Mercedes
K1 Matemáticas
K1 Álgebras de caminos de Leavitt, Álgebras de grafo, grafo dual
K1 1201.05 Campos, Anillos, Álgebras
AB We characterize, in terms of its idempotents, the Leavitt path algebras of an arbitrary graph that satisfies Condition (L) or Condition (NE). In the latter case, we also provide the structure of such algebras. Dual graph techniques are considered and demonstrated to be useful in the approach of the study of Leavitt path algebras of arbitrary graphs. A refining of the so-called Reduction Theorem is achieved and is used to prove that I(Pc(E)), the ideal of the vertices which are base of cycles without exits of the graph E, a construction with a clear parallelism to the socle, is a ring isomorphism invariant for arbitrary Leavitt path algebras. We also determine its structure in any case.
PB De Gruyter
SN 0933-7741
YR 2015
FD 2015
LK https://uvadoc.uva.es/handle/10324/66156
UL https://uvadoc.uva.es/handle/10324/66156
LA spa
NO Forum Mathematicum, 2015, vol. 27, no. 1, p. 601-633.
NO Producción Científica
DS UVaDOC
RD 11-jul-2024