The Hochschild cohomology groups for a family of local algebras of semidihedral type are calculated. The family occurs in the Erdmann classification only in the case where the characteristic of underlying field equals 2.
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A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups,” Algebra Analiz, 21, No. 2, 1–51 (2009).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. II. Local algebras,” Zap. Nauchn. Semin. POMI, 386, 144–202 (2011).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. III. The family SD(2B)2 in characteristic 2,” Zap. Nauchn. Semin. POMI, 400, 133–157 (2012).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. IV. The cohomology algebra for the family SD(2B)2(k, t, c) in the case c = 0,” Zap. Nauchn. Semin. POMI, 413, 45–92 (2003).
A. I. Generalov and I. M. Zilberbord, “Hochschild cohomology of algebras of semidihedral type. V. The family SD(3K),” Zap. Nauchn. Semin. POMI, 435, 5–32 (2015).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. VI. The family SD(2B)2 in characteristic different from 2,” Zap. Nauchn. Semin. POMI, 443, 61–77 (2016).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. VII. Algebras with a small parameter,” Zap. Nauchn. Semin. POMI, 452, 52–69 (2016).
A. I. Generalov and A. A. Zaikovskii, “On derived equivalence of algebras of semidihedral type with two simple modules,” Zap. Nauchn. Semin. POMI, 452, 70–85 (2016).
A. I. Generalov and A. A. Zaikovskii, “Hochschild cohomology of algebras of semidihedral type. VIII. The family SD(2B)1,” Zap. Nauchn. Semin. POMI, 460, 35–52 (2017).
K. Erdmann, Blocks of Tame Representation Type and Related Algebras, Lect. Notes Math., 1428, Berlin, Heidelberg (1990).
A. I. Generalov, “Cohomology of algebras of semidihedral type. VII. Local algebras,” Zap. Nauchn. Semin. POMI, 365, 130–142 (2009).
Yu. V. Volkov, A. I. Generalov, and S. O. Ivanov, “On construction of bimodule resolutions with the help of Happel’s lemma,” Zap. Nauchn. Semin. POMI, 375, 61–70 (2010).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 478, 2018, pp. 17–31.
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Generalov, A.I., Nikulin, D.A. Hochschild Cohomology of Algebras of Semidihedral Type. IX: Exceptional Local Algebras. J Math Sci 247, 507–517 (2020). https://doi.org/10.1007/s10958-020-04817-x
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DOI: https://doi.org/10.1007/s10958-020-04817-x