Hochschild Cohomology Groups of the Z_n Graded Algebras

In this note the definition of Hochschild cohomology groups of Z_n-graded algebras is given,and the low dimensional Hochschild cohomology groups are described.Moreover, a necessary and sufficient condition for a Z_n-graded algebra to be a graded separable algebra is given in terms of the first Hochschild cohomology group,and the one-to-one correspondence between the zero degree component of the second Hochschild cohomology group and the Hochschild extensions of A is obtained.