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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2023_522_a3,
     author = {A. I. Generalov and I. M. Zilberbord and V. A. Rogov},
     title = {Hochschild cohomology for algebras of dihedral type. {X.} {Exceptional} local algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--83},
     year = {2023},
     volume = {522},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a3/}
}
TY  - JOUR
AU  - A. I. Generalov
AU  - I. M. Zilberbord
AU  - V. A. Rogov
TI  - Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 60
EP  - 83
VL  - 522
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a3/
LA  - ru
ID  - ZNSL_2023_522_a3
ER  - 
%0 Journal Article
%A A. I. Generalov
%A I. M. Zilberbord
%A V. A. Rogov
%T Hochschild cohomology for algebras of dihedral type. X. Exceptional local algebras
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 60-83
%V 522
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a3/
%G ru
%F ZNSL_2023_522_a3
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/

[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