Geodesic
Hochschild cohomology for nonstandard self-injective algebras of tree class $D_n$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 21, Tome 388 (2011), pp. 48-99 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We construct minimal projective bimodule resolutions for nonstandard self-injective algebras of finite representation type. Further, using this resolution we calculate dimensions of the Hochschild cohomology groups and describe Hochschild cohomology algebra in terms of generators and relations. The above resolution, and thus also the Hochschild cohomology of these algebras, are periodic. 
@article{ZNSL_2011_388_a2,
     author = {Y. V. Volkov},
     title = {Hochschild cohomology for nonstandard self-injective algebras of tree class~$D_n$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {48--99},
     year = {2011},
     volume = {388},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a2/}
}
TY  - JOUR
AU  - Y. V. Volkov
TI  - Hochschild cohomology for nonstandard self-injective algebras of tree class $D_n$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 48
EP  - 99
VL  - 388
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a2/
LA  - ru
ID  - ZNSL_2011_388_a2
ER  - 
%0 Journal Article
%A Y. V. Volkov
%T Hochschild cohomology for nonstandard self-injective algebras of tree class $D_n$
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 48-99
%V 388
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a2/
%G ru
%F ZNSL_2011_388_a2
Y. V. Volkov. Hochschild cohomology for nonstandard self-injective algebras of tree class $D_n$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 21, Tome 388 (2011), pp. 48-99. http://geodesic.mathdoc.fr/item/ZNSL_2011_388_a2/

[1] C. Riedtmann, “Algebren, Darstellungsköcher, Überlagerungen und zurück”, Comment. Math. Helv., 55 (1980), 199–224 | DOI | MR | Zbl

[2] C. Riedtmann, “Representation-finite self-injective algebras of class $A_n$”, Lect. Notes Math., 832, 1980, 449–520 | DOI | MR | Zbl

[3] K. Erdmann, T. Holm, “Twisted bimodules and Hochschild cohomology for self-injective algebras of class $A_n$”, Forum Math., 11 (1999), 177–201 | DOI | MR | Zbl

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

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

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

[7] Yu. V. Volkov, “Klassy stabilnoi ekvivalentnosti samoin'ektivnykh algebr drevesnogo tipa $D_n$”, Vestnik SPb. un-ta, Ser. 1, Mat., mekh., astr., 2008, no. 1, 15–21 | Zbl

[8] 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

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

[10] 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

[11] K. Erdmann, A. Skowroński, “Periodic algebras”, Trends in Representation Theory and Related Topics, European Math. Soc., Zurich, 2008, 201–251 | DOI | MR | Zbl

[12] A. S. Dugas, “Periodic resolutions and self-injective algebras of finite type”, J. Pure and Applied Algebra, 214:6 (2010), 990–1000 | DOI | MR | Zbl

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