CLASSIFICATION OF LEAVITT PATH ALGEBRAS WITH TWO VERTICES
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Dosyalar
Tarih
2019
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Independent Univ Moscow-Ium
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 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.
Açıklama
Kanuni, Muge/0000-0001-7436-039X
WOS: 000476630800004
WOS: 000476630800004
Anahtar Kelimeler
Leavitt path algebra, IBN property, type, socle, extreme cycle, K-0
Kaynak
Moscow Mathematical Journal
WoS Q Değeri
Q4
Scopus Q Değeri
Q2
Cilt
19
Sayı
3
