A combinatorial discussion on finit edimensional Leavitt path algebras

KOÇ A., ESİN S., GÜLOĞLU İ., KANUNİ M.

Hacettepe Journal of Mathematics and Statistics, cilt.43, sa.6, ss.943-951, 2014 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 6
  • Basım Tarihi: 2014
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.943-951
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

AnyfinitedimensionalsemisimplealgebraAoverafieldKisisomorphictoadirectsumoffinitedimensionalfullmatrixringsoversuitabledivisionrings.Weshallconsiderthedirectsumoffinitedimensionalfullmatrixringsoverafield K. AllsuchfinitedimensionalsemisimplealgebrasariseasfinitedimensionalLeavittpathalgebras.Forthisspecificfinitedimensionalsemisimplealgebra A overafield K, wedefineauniquelydeterminedspecificgraph-calledatruncatedtreeassociatedwith A -whoseLeavittpathalgebraisisomorphicto A .Wedefineanalgebraicinvariant κ( A ) for A andcountthenumberofisomorphismclassesofLeavittpathalgebraswiththesamefixedvalueof κ(A ).Moreover,wefindthemaximumandtheminimum K-dimensionsoftheLeavittpathalgebrasofpossibletreeswithagivennumberofverticesandwealsodeterminethenumberofdistinctLeavittpathalgebrasoflinegraphswithagivennumberofvertices.