A combinatorial discussion on ?nit edimensional Leavitt path algebras
Yükleniyor...
Dosyalar
Tarih
2014
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Any finite dimensional semisimple algebra A over a field K is isomorphicto a direct sum of finite dimensional full matrix rings over suitabledivision rings. We shall consider the direct sum of finite dimensionalfull matrix rings over a fieldK:All such finite dimensional semisimplealgebras arise as finite dimensional Leavitt path algebras. For thisspecific finite dimensional semisimple algebraAover a fieldK;we definea uniquely determined specific graph - called a truncated tree associatedwithA- whose Leavitt path algebra is isomorphic toA. We define analgebraic invariant (A)forAand count the number of isomorphismclasses of Leavitt path algebras with the same fixed value of (A).Moreover, we find the maximum and the minimumK-dimensions of theLeavitt path algebras of possible trees with a given number of verticesand we also determine the number of distinct Leavitt path algebras ofline graphs with a given number of vertices.
Açıklama
Anahtar Kelimeler
İstatistik ve Olasılık, Matematik
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
43
Sayı
6
