On a class of algebras associated to directed graphs

Israel Gelfand, Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson

Research output: Contribution to journalArticle

17 Scopus citations


To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over noncommutative algebras. We also construct a basis for our algebras associated to layered graphs.

Original languageEnglish (US)
Pages (from-to)281-295
Number of pages15
JournalSelecta Mathematica, New Series
Issue number2
StatePublished - Jun 1 2005

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Mathematics(all)


  • Directed graphs
  • Linear bases
  • Noncommutative algebras

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