Geodesic
Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 60-83 
A. I. Generalov; I. M. Zilberbord; V. A. Rogov. Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 60-83. http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a3/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The Hochschild cohomology groups are computed for “exceptional” local algebras of dihedral type (from the famous K. Erdmann's classification) which appear when the base field has characteristic 2. In the calculation, we use the beforehand construction of the bimodule resolution for the algebras in question.

[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

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

[3] 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 | Zbl

[4] 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

[5] 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

[6] 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

[7] A. I. Generalov, M. A. Filippov, “Kogomologii Khokhshilda algebr diedralnogo tipa, VII. Seriya $D(3\mathcal R)$”, Zap. nauchn. semin. POMI, 460, 2017, 53–81

[8] A. I. Generalov, N. Yu. Kosovskaya, “Kogomologii Khokhshilda algebr diedralnogo tipa, VIII. Algebra kogomologii dlya serii $D(2\mathcal B)(k,s,0)$ v kharakteristike 2”, Zap. nauchn. semin. POMI, 470, 2018, 50–87

[9] A. I. Generalov, M. A. Kachalova, P. A. Mostovskii, “Kogomologii Khokhshilda algebr diedralnogo tipa, IX. Algebra kogomologii dlya serii $D(3\mathcal K)$ v kharakteristike, otlichnoi ot $2$”, Zap. nauchn. semin. POMI, 513, 2022, 30–56

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

[11] D. Happel, “Hochschild cohomology of finite-dimensional algebras”, Lect. Notes Math., 1404, 1989, 108–126 | DOI | MR | Zbl

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

[13] 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 | Zbl

[14] 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

[15] M. A. Kachalova, “Algebra kogomologii Khokhshilda isklyuchitelnykh lokalnykh algebr diedralnogo tipa”, Zap. nauchn. semin. POMI, 513, 2022, 85–109 | MR