TL;DR
This paper explores N-Koszul graded algebras with a single relation, providing new criteria and examples using Gerasimov's theorem, along with an alternative proof for the N=2 case and results on Calabi-Yau algebras.
Contribution
It introduces a new criterion for N-Koszulity in algebras with one relation and offers an alternative proof of Gerasimov's theorem for N=2, expanding understanding of these structures.
Findings
New criterion for N-Koszul algebras with one relation
Provided new examples of N-Koszul algebras
Proved related results on Calabi-Yau algebras
Abstract
The paper is devoted to graded algebras having a single homogeneous relation. Using Gerasimov's theorem, a criterion to be N-Koszul is given, providing new examples. An alternative proof of Gerasimov's theorem for N=2 is given. Some related results on Calabi-Yau algebras are proved.
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