Gerasimov's theorem and N-Koszul algebras

• Autores: Roland Berger
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 79, Nº 3, 2009, págs. 631-648
• Idioma: inglés
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• Resumen

  • This article is devoted to graded algebras A having a single homogeneous relation. We give a criterion for A to be N-Koszul, where N is the degree of the relation. This criterion uses a theorem of Gerasimov. As a consequence of the criterion, some new examples of N-Koszul algebras are presented. We give an alternative proof of Gerasimov�s theorem for N = 2, which is related to Dubois-Violette�s theorem concerning a matrix description of the Koszul and ASGorenstein algebras of global dimension 2. We determine which of the Poincar´e�Birkhoff�Witt deformations of a symplectic form are Calabi�Yau.