(a,b,c)-Koszul Algebras

Given fixed integers a; b and c with a c b 1, the notion of (a;b;c)-Koszul algebra is introduced, which is another extension of Koszul algebras and includes some Artin-Schelter regular algebras of global dimension five as special examples. Some criteria for a standard graded algebra to be (a,b,c)-Koszul are given. Further, the Yoneda algebras and the H-Galois graded extensions of (a,b,c)-Koszul algebras are discussed, where H is a finite dimensional semisimple and cosemisimple Hopf algebra. Moreover, the so-called (generalized) (a,b,c)-Koszul modules are introduced and some basic properties are also provided.