A combinatorial discussion on finite dimensional Leavitt path algebras
Yükleniyor...
Dosyalar
Tarih
2014
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Hacettepe Univ, Fac Sci
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. We shall consider the direct sum of finite dimensional full matrix rings over a field K. All such finite dimensional semisimple algebras arise as finite dimensional Leavitt path algebras. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely determined specific graph - called a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant kappa(A) for A and count the number of isomorphism classes of Leavitt path algebras with the same fixed value of kappa(A). Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras. of possible trees with a given number of vertices and we also determine the number of distinct Leavitt path algebras of line graphs with a given number of vertices.
Açıklama
Kanuni, Muge/0000-0001-7436-039X;
WOS: 000348691000006
WOS: 000348691000006
Anahtar Kelimeler
Finite dimensional semisimple algebra, Leavitt path algebra, Truncated trees, Line graphs
Kaynak
Hacettepe Journal Of Mathematics And Statistics
WoS Q Değeri
Q4
Scopus Q Değeri
N/A
Cilt
43
Sayı
6
