Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 74-102 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We compute the Hochschild cohomology groups for algebras of dihedral type which form the family $D(3\mathcal K)$ (from the famous K. Erdmann's classification) over an algebraically closed field with characteristic different from 2. In the calculation, we use the beforehand construction of the bimodule resolution for algebras from the family under discussion.
@article{ZNSL_2014_430_a7,
     author = {A. I. Generalov and I. M. Zilberbord and D. B. Romanova},
     title = {Hochschild cohomology for algebras of dihedral {type.~V.} {The} family $D(3\mathcal K)$ in characteristic different from~2},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {74--102},
     year = {2014},
     volume = {430},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a7/}
}
TY  - JOUR
AU  - A. I. Generalov
AU  - I. M. Zilberbord
AU  - D. B. Romanova
TI  - Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 74
EP  - 102
VL  - 430
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a7/
LA  - ru
ID  - ZNSL_2014_430_a7
ER  - 
%0 Journal Article
%A A. I. Generalov
%A I. M. Zilberbord
%A D. B. Romanova
%T Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 74-102
%V 430
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a7/
%G ru
%F ZNSL_2014_430_a7
A. I. Generalov; I. M. Zilberbord; D. B. Romanova. Hochschild cohomology for algebras of dihedral type. V. The family $D(3\mathcal K)$ in characteristic different from 2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 74-102. http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a7/

[1] 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

[2] K. Erdmann, Blocks of tame representation type and related algebras, Lect. Notes Math., 1428, 1990 | MR | Zbl

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

[4] 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

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

[6] 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

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

[8] 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

[9] 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

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

[13] 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

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

[15] 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

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

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

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

[19] 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

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

[21] 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

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

[23] 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

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

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

[26] M. A. Pustovykh, “Koltso kogomologii Khokhshilda samoin'ektivnykh algebr drevesnogo tipa $E_6$”, Zap. nauchn. semin. POMI, 423, 2014, 205–243

[27] Yu. V. Volkov, A. I. Generalov, S. O. Ivanov, “O postroenii bimodulnykh rezolvent s pomoschyu lemmy Khappelya”, Zap. nauchn. semin. POMI, 375, 2010, 61–70 | MR | Zbl

[28] O. I. Balashov, A. I. Generalov, “Kogomologii algebr diedralnogo tipa. II”, Algebra i analiz, 13:1 (2002), 3–25 | MR | Zbl