Decomposition Of A Projection Almost Koszul Algebra Extraordinary Expansion Since The Incident

Almost Koszul algebra is the generalization of Koszul algebra. Almost Koszul algebra is a important class of cycle algebra, in terms of it, we prove the following theorem. Theorem3.2Let A be a left (p,q)-Koszul self-injection algebra with p,q≥2, then cx (A)=1.We also studied the radical cube zero self-injection algebra given by type A3double quiver, it is a almost Koszul algebra, we calculate a mininal proje-ctive resolution of single module in the trivial extension A, to further certify:Theorem3.3(1) A is not almost Koszul;(2) CX(A)=2, so CX(A)-CX(A)+1.