The Hochschild cohomology ring for self-injective algebras of tree class E8 with finite representation type is described in terms of generators and relations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Riedtmann, “Algebren, Darstellungsköcher, Überlagerungen und zurück,” Comment. Math. Helv., 55, 199–224 (1980).
K. Erdmann and T. Holm, “Twisted bimodules and Hochschild cohomology for selfinjective algebras of class An,” Forum Math. 11, 177–201 (1999).
A. I. Generalov and M. A. Kachalova, “Bimodule Resolution of Möbius Algebras,” Zap. Nauchn. Semin. POMI, 321, 36–66 (2005).
M. A. Kachalova, “Hochschild cohomology of Möbius Algebras,” Zap. Nauchn. Semin. POMI, 330, 173–200 (2006).
M. A. Pustovykh, “Hochschild cohomology ring of Möbius algebras,” Zap. Nauchn. Semin. POMI, 388, 210–246 (2011).
Yu. V. Volkov and A. I. Generalov, “Hochschild cohomology for self-injective algebras of tree class Dn. I,” Zap. Nauchn. Semin. POMI, 343, 121–182 (2007).
Yu. V. Volkov, “Hochschild cohomology for self-injective algebras of tree class Dn. II,” Zap. Nauchn. Semin. POMI, 365, 63–121 (2009).
Yu. V. Volkov and A. I. Generalov, “Hochschild cohomology for self-injective algebras of tree class Dn. III,” Zap. Nauchn. Semin. POMI, 386, 100–128 (2011).
Yu. V. Volkov, “Hochschild cohomology for nonstandard self-injective algebras of tree class Dn,” Zap. Nauchn. Semin. POMI, 388, 48–99 (2011).
Yu. V. Volkov, “Hochschild cohomology for self-injective algebras of tree class Dn. IV,” Zap. Nauchn. Semin. POMI, 388, 100–118 (2011).
Yu. V. Volkov, “Hochschild cohomology for self-injective algebras of tree class Dn. V,” Zap. Nauchn. Semin. POMI, 394, 140–173 (2011).
M. A. Pustovykh, “Hochschild cohomology ring for self-injective algebras of tree class E6,” Zap. Nauchn. Semin. POMI, 423, 205–243 (2014).
M. A. Kachalova, “Hochschild cohomology ring for self-injective algebras of tree class E6. II,” Zap. Nauchn. Semin. POMI, 478, 128–171 (2019).
M. A. Kachalova, “Hochschild cohomology ring for self-injective algebras of tree class E7,” Zap. Nauchn. Semin. POMI, 484, 86–114 (2019).
D. Happel, “Hochschild cohomology of finite-dimensional algebras,” Lect. Notes Math., 1404, 108–126 (1989).
Yu. V. Volkov, A. I. Generalov, and S. O. Ivanov, “On construction of bimodule resolutions with the help of Happel’s lemma,” Zap. Nauchn. Semin. POMI, 375, 61–70 (2010).
M. Kachalova, “Hochschild cohomology rings for self-injective algebras of tree classes E7 and E8,” arXiv: 1910.03043 (2021).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 500, 2021, pp. 112–148.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kachalova, M.A. Hochschild Cohomology Ring for Self-Injective Algebras of Tree Class E8. J Math Sci 272, 418–443 (2023). https://doi.org/10.1007/s10958-023-06433-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06433-x