Semigroup C*-algebras and toric varieties

  • Joachim Cuntz
Part of the Oberwolfach Seminars book series (OWS, volume 47)


Let S be a finitely generated subsemigroup of \(\mathbb{Z}^n\). Then its monoid algebra \(\mathbb{C}S\) is a finitely generated C-algebra with no nonzero nilpotent elements. It is therefore the coordinate ring of an affine variety over \(\mathbb{C}\). Such varieties are called affine toric varieties (they carry an action of an n-dimensional torus). Of course, here we may replace \(\mathbb{C}\) by an arbitrary field. General references for toric varieties and the corresponding semigroups are, for instance, [CLS11] or [Nee92].


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Joachim Cuntz
    • 1
  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany

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