Geodesic
Selfinjective algebras of stable Calabi--Yau dimension three
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 226-261

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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. 
@article{ZNSL_2011_394_a8,
     author = {S. O. Ivanov},
     title = {Selfinjective algebras of stable {Calabi--Yau} dimension three},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {226--261},
     publisher = {mathdoc},
     volume = {394},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a8/}
}
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S. O. Ivanov. Selfinjective algebras of stable Calabi--Yau dimension three. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 226-261. http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a8/