Abstract
The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called (s, t, d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An (s, t, d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of an (s, t, d)-bi-Koszul algebra is discussed. Based on it, the notion of strongly (s, t, d)-bi-Koszul algebras is raised and their homological properties are further discussed.
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