Quivers of monoids with basic algebras

Stuart Margolis, Benjamin Steinberg

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23 Scopus citations


We compute the quiver of any finite monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term rectangular monoids (in the semigroup theory literature the class is known as DO) to representation-theoretic computations for group algebras of maximal subgroups. Hence in good characteristic for the maximal subgroups, this gives an essentially complete computation. Since groups are examples of rectangular monoids, we cannot hope to do better than this. For the subclass of R-trivial monoids, we also provide a semigroup-theoretic description of the projective indecomposable modules and compute the Cartan matrix.

Original languageEnglish
Pages (from-to)1516-1560
Number of pages45
JournalCompositio Mathematica
Issue number5
StatePublished - Sep 2012


  • EI-categories
  • Hochschild-Mitchell cohomology
  • Monoids
  • Quivers
  • Representation theory


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