Gerasimovs theorem and N-Koszul algebras

June 2009
Journal of the London Mathematical Society;Jun2009, Vol. 79 Issue 3, p631
Academic Journal
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 Gerasimovs theorem for N = 2, which is related to Dubois-Violettes theorem concerning a matrix description of the Koszul and AS-Gorenstein algebras of global dimension 2. We determine which of the Poincaré–Birkhoff–Witt deformations of a symplectic form are Calabi–Yau.


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