Rigidity dimensions of Hochschild extensions of hereditary algebras of type D

Rigidity dimension of algebras is a new homological dimension which measures the quality of resolutions of algebras by algebras of finite global dimension and large dominant dimension. In this paper, we calculate the rigidity dimension of the Hochschild extension of a hereditary algebra H of Dynkin type Dn(n≥4) by the standard duality H-bimodule. It turns out that this dimension is independent of n and the orientation of Dn.