Geodesic
Hochschild cohomology of algebras of dihedral type. II. Local algebras
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 92-129 
A. I. Generalov. Hochschild cohomology of algebras of dihedral type. II. Local algebras. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 92-129. http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a6/
@article{ZNSL_2010_375_a6,
     author = {A. I. Generalov},
     title = {Hochschild cohomology of algebras of dihedral {type.~II.} {Local} algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {92--129},
     year = {2010},
     volume = {375},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For local algebras which constitute a family of algebras of dihedral type, we calculate the Hochschild cohomology in the case where the base algebraically closed field has a characteristic different from 2. Furthermore, we give a description of the Hochschild cohomology algebra (in terms of generators and relations) for the local algebras under consideration. We use in the corresponding calculation a beforehand constructed bimodule resolution for these algebras. Bibl. – 19 titles.

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

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

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

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

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

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

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

[8] 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

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

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

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

[12] A. I. Generalov, “Kogomologii algebr diedralnogo tipa, I”, Zap. nauchn. semin. POMI, 265, 1999, 139–162 | MR | Zbl

[13] A. I. Generalov, “Kogomologii algebr poludiedralnogo tipa, I”, Algebra i analiz, 13:4 (2001), 54–85 | MR | Zbl

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

[15] A. I. Generalov, “Kogomologii Khokhshilda algebr diedralnogo tipa. III. Lokalnye algebry v kharakteristike 2”, Vestnik S.-Peterburgskogo un-ta, 2010 (to appear) | Zbl

[16] S. Eilenberg, S. MacLane, “Cohomology theory in abstract groups, I”, Ann. Math., 48 (1947), 51–78 | DOI | MR | Zbl

[17] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, M., 1960

[18] M. Gerstenhaber, “The cohomology structure of an associative ring”, Ann. Math., 78 (1963), 267–288 | DOI | MR | Zbl

[19] M. Gerstenhaber, S. D. Schack, “Algebraic cohomology and deformation theory”, Deformation theory of algebras and structures and applications, NATO ASI Ser., Ser. C: Math. and Phys. Sci., 247, eds. M. Hazewinkel, M. Gerstenhaber, Kluwer Acad. Publ., 1988, 11–264 | MR