Finite generation for Hochschild cohomology of Gorenstein monomial algebras

• Vladimir Dotsenko ^[1] ; Vincent Gélinas ^[2] ; Pedro Tamaroff ^[3]
  1. [1] University of Strasbourg

     University of Strasbourg

     Arrondissement de Strasbourg-Ville, Francia

     
  2. [2] University of Toronto

     University of Toronto

     Canadá

     
  3. [3] Humboldt University of Berlin

     Humboldt University of Berlin

     Berlin, Stadt, Alemania

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 1, 2023
• Idioma: inglés
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• Resumen

  • We show that a finite dimensional monomial algebra satisfies the finite generation conditions of Snashall–Solberg for Hochschild cohomology if and only if it is Gorenstein. This gives, in the case of monomial algebras, the converse to a theorem of Erdmann–Holloway–Snashall–Solberg–Taillefer. We also give a necessary and sufficient combinatorial criterion for finite generation.