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The main result of this paper is the following: Let A be a self-injective Nakayama K-algebra, which is basic and connected. Suppose that A is a right Aemodule of TAe-period 1. (1) If A is an algebra whose Jacobson radical square is zero,then A(TAe; A) ≌ K[Z]. (2) If A is an algebra whose Jacobson radical square is not zero,then A(TAe ;A) ≌ K[X, Z]/(Xn) for some positive integer n.