The Minimal Projective Resolution Of Selfinjective Algebras

Almost Koszul algebra is Koszul algebra, almost Koszul self-injective algebra is a kind of important periodic algebra. Let (kAn)! is a linear direct-ion An type Dynkin graphs path algebraic quadratic dual algebra, its trivi-al extension T(kAn)! is a root of three parties is zero almost Koszul algebra. we depict the algebra the trivial extension of algebra TT(kAn)! corresponds to An source point of simple-module Si minimal projective resolution, and depicts its complexity. got:Theorem 3.2.1 Let…â†' P(s)(S1)fsâ†'…â†'P(1)(S1)f1â†'S1â†'0 for algebra A simple module S1 minimal projective resolution,then i≥ 0.1< k< n.Thus proved:Theorem 3.2.2 CXΛ(S1)= 2.corollary 3.2.1 CX(Λ)≥ 2 and Λ is not almost Koszul algebra.