A combinatorial discussion on finit edimensional Leavitt path algebras

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

Hacettepe Journal of Mathematics and Statistics, vol.43, no.6, pp.943-951, 2014 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 6
  • Publication Date: 2014
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.943-951
  • Istanbul Kültür University Affiliated: Yes

Abstract

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.