For an R-bimodule M with structure of a k-algebra and an agreed action of a finite group G ⊂ AutR, an algebra HH*(R,M)G↑ is defined. An isomorphism between the algebras HH*(R) and HH* \( {\left(\tilde{R},\tilde{R}\#kG\right)}^{G\uparrow } \) is constructed in terms of bar-resolutions, where \( \tilde{R}=R\#k{G}^{\ast } \). The Hochschild cohomology algebra for one series of the self-injective algebras of tree class D n is calculated with the help of these results. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, pp. 33–56.
Translated by Yu. V. Volkov.
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Volkov, Y.V. Hochschild Cohomology for Self-Injective Algebras of Tree Class D n . VI. J Math Sci 209, 500–514 (2015). https://doi.org/10.1007/s10958-015-2508-0
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DOI: https://doi.org/10.1007/s10958-015-2508-0