Koszulity for Nonquadratic Algebras

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Poincaré-Birkhoff-Witt deformations of Calabi-Yau algebras (2006, background): “n 1/-Koszul of global dimension 3 [2], Theorem 3.”
Koszul and Gorenstein Properties for Homogeneous Algebras (2003, background): “The appearance of noncommutative projective geometry has given a new impulse to the study of (noncommutative) graded algebras [20].”
Superpotentials and higher order derivations (2008, background): “N -Koszul situation in accordance with the result from [ 4 ] and [6].”
δ-Koszul Algebras (2005, methodology): “Also included in this class are the D-Koszul algebras introduced by Berger (2001) and later studied by Green et al. For D-Koszul algebras, there is some d such that n = n 2 d for n even, n− 1 2 d + 1 for n odd.”
Generalizing the notion of Koszul algebra (2007, background): “Several works ([3], [8], [4], [7] among others) demonstrate similarities between N -Koszul algebras and Koszul algebras, and so provide evidence that the N -Koszul algebras should be included in a generalization of Koszulity.”