Hochschild Cohomology of One Class of the Quasi-entwining Structure

In this paper, we discuss the Hochschild cohomology of the quasi-entwining structure of a truncated quiver algebra A and its dual coalgebra. For the quasi-entwining structure of this kind of algebra A and eoalgebra C=A*, we give the calculations of its Hochsehild cohomology groups, and moreover, we obtain that its Hochsehild eohomology group is trivial if and only if C⊗A is an injective C- bieomodule.