“…As examples, we show how our theory is applied to in the path algebras of Dynkin type, and to Iyama's absolute n-complete algebra T n m (k) for m = 4 and n = 0, 1. In a forthcoming paper [18], we study certain classes of n-translation algebras which include the quadratic dual of Iyama's absolute n-complete algebra T n m (k). From the viewpoint of algebras, our n-translation algebras look like a quadratic dual version of algebras in n-representation theory [21,22,23,24,20].…”