Hochschild cohomology for algebras of semidihedral type.  VI. The family $SD(2\mathcal B)_2$ in characteristic different from 2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 61-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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We compute the Hochschild cohomology groups for algebras of semidihedral type contained in the family $SD(2\mathcal B)_2$ (of the famous K. Erdmann's classification) over an algebraically closed field of characteristic $\neq2$. In the calculation, we use the minimal projective bimodule resolution for algebras from the above family constructed in the previous paper by the author.
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A. I. Generalov. Hochschild cohomology for algebras of semidihedral type.  VI. The family $SD(2\mathcal B)_2$ in characteristic different from 2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 61-77. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a5/

[1] K. Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Math., 1428, Berlin–Heidelberg, 1990 | MR | Zbl

[2] A. I. Generalov, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, III. Seriya $SD(2\mathcal B)_2$ v kharakteristike $2$”, Zap. nauchn. semin. POMI, 400, 2012, 133–157 | MR

[3] A. I. Generalov, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, IV. Algebra kogomologii dlya serii $SD(2\mathcal B)_2(k,t,c)$ pri $c=0$”, Zap. nauchn. semin. POMI, 413, 2013, 45–92 | MR

[4] A. I. Generalov, “Kogomologii Khokhshilda algebr diedralnogo tipa, I: seriya $D(3\mathcal K)$ v kharakteristike $2$”, Algebra i analiz, 16:6 (2004), 53–122 | MR | Zbl

[5] A. I. Generalov, “Kogomologii Khokhshilda algebr diedralnogo tipa, II. Lokalnye algebry”, Zap. nauchn. semin. POMI, 375, 2010, 92–129 | MR | Zbl

[6] A. I. Generalov, “Kogomologii Khokhshilda algebr diedralnogo tipa, III. Lokalnye algebry v kharakteristike 2”, Vestnik S.-Peterburgskogo un-ta. Ser. 1. Mat., mekh., astron., 2010, no. 1, 28–38 | MR | Zbl

[7] A. I. Generalov, N. Yu. Kosovskaya, “Kogomologii Khokhshilda algebr diedralnogo tipa, IV. Seriya $D(2\mathcal B)(k,s,0)$”, Zap. nauchn. semin. POMI, 423, 2014, 67–104

[8] A. I. Generalov, I. M. Zilberbord, D. B. Romanova, “Kogomologii Khokhshilda algebr diedralnogo tipa, V. Seriya $D(3\mathcal K)$ v kharakteristike, otlichnoi ot $2$”, Zap. nauchn. semin. POMI, 430, 2014, 74–102

[9] A. I. Generalov, D. B. Romanova, “Kogomologii Khokhshilda algebr diedralnogo tipa, VI. Seriya $D(2\mathcal B)(k,s,1)$”, Algebra i analiz, 27:6 (2015), 89–116

[10] A. I. Generalov, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, I. Gruppovye algebry poludiedralnykh grupp”, Algebra i analiz, 21:2 (2009), 1–51 | MR | Zbl

[11] A. I. Generalov, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, II. Lokalnye algebry”, Zap. nauchn. semin. POMI, 386, 2011, 144–202 | MR

[12] A. I. Generalov, I. M. Zilberbord, “Kogomologii Khokhshilda algebr poludiedralnogo tipa, V. Seriya $SD(3\mathcal K)$”, Zap. nauchn. semin. POMI, 435, 2015, 5–32

[13] A. I. Generalov, “Kogomologii Khokhshilda algebr kvaternionnogo tipa, I: obobschennye gruppy kvaternionov”, Algebra i analiz, 18:1 (2006), 55–107 | MR | Zbl

[14] A. I. Generalov, A. A. Ivanov, S. O. Ivanov, “Kogomologii Khokhshilda algebr kvaternionnogo tipa, II. Seriya $Q(2\mathcal B)_1$ v kharakteristike $2$”, Zap. nauchn. semin. POMI, 349, 2007, 53–134

[15] A. I. Generalov, “Kogomologii Khokhshilda algebr kvaternionnogo tipa, III. Algebry s malym parametrom”, Zap. nauchn. semin. POMI, 356, 2008, 46–84 | MR | Zbl

[16] A. A. Ivanov, “Kogomologii Khokhshilda algebr kvaternionnogo tipa: seriya $Q(2\mathcal B)_1(k,s,a,c)$ nad polem kharakteristiki ne 2”, Vestnik S.-Peterburgskogo un-ta. Ser. 1. Mat., mekh., astron., 2010, no. 1, 63–72 | Zbl

[17] A. I. Generalov, N. Yu. Kosovskaya, “Kogomologii Khokhshilda algebr Lyu–Shultsa”, Algebra i analiz, 18:4 (2006), 39–82 | MR | Zbl

[18] K. Erdmann, Th. Holm, N. Snashall, “Twisted bimodules and Hochschild cohomology for self-injective algebras of class $A_n$. II”, Algebras and Repr. Theory, 5 (2002), 457–482 | DOI | MR | Zbl

[19] A. I. Generalov, M. A. Kachalova, “Bimodulnaya rezolventa algebry Mëbiusa”, Zap. nauchn. semin. POMI, 321, 2005, 36–66 | MR | Zbl

[20] M. A. Kachalova, “Kogomologii Khokhshilda algebry Mëbiusa”, Zap. nauchn. semin. POMI, 330, 2006, 173–200 | MR | Zbl

[21] M. A. Pustovykh, “Koltso kogomologii Khokhshilda algebry Mëbiusa”, Zap. nauchn. semin. POMI, 388, 2011, 210–246 | MR

[22] Yu. V. Volkov, A. I. Generalov, “Kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $D_n$. I”, Zap. nauchn. semin. POMI, 343, 2007, 121–182 | MR

[23] Yu. V. Volkov, “Kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $D_n$. II”, Zap. nauchn. semin. POMI, 365, 2009, 63–121 | MR | Zbl

[24] Yu. V. Volkov, A. I. Generalov, “Kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $D_n$. III”, Zap. nauchn. semin. POMI, 386, 2011, 100–128 | MR

[25] Yu. V. Volkov, “Kogomologii Khokhshilda nestandartnykh samoin'ektivnykh algebr drevesnogo tipa $D_n$”, Zap. nauchn. semin. POMI, 388, 2011, 48–99 | MR

[26] Yu. V. Volkov, “Algebra kogomologii Khokhshilda dlya odnoi serii samoin'ektivnykh algebr drevesnogo tipa $D_n$”, Algebra i analiz, 23:5 (2011), 99–139 | MR

[27] Yu. V. Volkov, “Kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $D_n$. IV”, Zap. nauchn. semin. POMI, 388, 2011, 100–118 | MR

[28] Yu. V. Volkov, “Kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $D_n$. V”, Zap. nauchn. semin. POMI, 394, 2011, 140–173 | MR

[29] Yu. V. Volkov, “Kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $D_n$. VI”, Zap. nauchn. semin. POMI, 423, 2014, 33–56

[30] A. I. Generalov, “Kogomologii Khokhshilda tselochislennogo gruppovogo koltsa diedralnoi gruppy. I. Chëtnyi sluchai”, Algebra i analiz, 19:5 (2007), 70–123 | MR | Zbl

[31] A. I. Generalov, “Kogomologii Khokhshilda tselochislennogo gruppovogo koltsa poludiedralnoi gruppy”, Zap. nauchn. semin. POMI, 388, 2011, 119–151 | MR

[32] T. Hayami, “Hochschild cohomology ring of the integral group ring of dihedral groups”, Tsukuba J. Math., 31 (2007), 99–127 | MR | Zbl

[33] T. Hayami, “Hochschild cohomology ring of the integral group ring of the semidihedral $2$-groups”, Algebra Colloq., 18:2 (2011), 241–258 | DOI | MR | Zbl