(a,b)-Koszul algebras

Let $a$ and $b$ be two integers such that $2\le a<b$. In this article we define the notion of $(a,b)$-Koszul algebra as a generalization of $N$-Koszul algebras. We also exhibit examples and we provide a minimal graded projective resolution of the algebra $A$ considered as an $A$-bimodule, which allows us to compute the Hochschild homology groups for some examples of $(a,b)$-Koszul algebras.