Selfinjective algebras of stable Calabi–Yau dimension three

In the present paper, we introduce the class of algebras, which allows the so-called DTI-family of relations. With few exceptions, the stable Calabi–Yau dimension of these algebras is equal to 3. We prove that all algebras of quaternion type are contained in this class, and we give some other examples of such algebras. Furthermore, we describe minimal projective bimodule resolutions for algebras from this class.