Geodesic
Hochschild cohomology for self-injective algebras of tree class~$D_n$.~I
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 121-182

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The minimal projective bimodule resolution is constructed for algebras in a family of selfinjective algebras of finite representation type and with tree class $D_n$. Using this resolution we calculate dimensions of the Hochschild cohomology groups for the algebras under consideration. The described resolution is periodic, and hence, the Hochschild cohomology of these algebras is periodic too. 
@article{ZNSL_2007_343_a4,
     author = {Yu. V. Volkov and A. I. Generalov},
     title = {Hochschild cohomology for self-injective algebras of tree class~$D_n${.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {343},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a4/}
}
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Yu. V. Volkov; A. I. Generalov. Hochschild cohomology for self-injective algebras of tree class~$D_n$.~I. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 15, Tome 343 (2007), pp. 121-182. http://geodesic.mathdoc.fr/item/ZNSL_2007_343_a4/