Gerasimov's theorem and N-Koszul 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.

19 pages; some corrections and improvements; version to appear

References in corpus (4)

• Calabi-Yau algebras
• PBW-deformations of N-Koszul algebras
• Homogeneous algebras, statistics and combinatorics
• Noncommutative Tangent Cones and Calabi Yau Algebras

Cited by in corpus (11)

• Crossed-products of Calabi-Yau algebras by finite groups
• Note on Nakayama automorphisms of PBW deformations and Hopf actions
• Deformations of Koszul Artin-Schelter Gorenstein algebras
• A criterion for homogeneous potentials to be 3-Calabi-Yau
• Graded 3-Calabi-Yau algebras as Ore extensions of 2-Calabi-Yau algebras
• Cocommutative Calabi-Yau Hopf algebras and deformations
• A Parametric Family of Subalgebras of the Weyl Algebra III. Derivations
• Calabi-Yau algebras viewed as deformations of Poisson algebras
• Skew Calabi-Yau property of normal extensions
• Generalized $d$-Koszul modules
• Categorical non-properness in wrapped Floer theory