The Hochschild cohomology ring of a Möbius algebras is described in terms of generators and relations. Bibliography: 22 titles.
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References
C. Riedtmann, “ Representation-finite self-injective algebras of class A n ,” Lect. Notes Math., 832, 449–520 (1980).
A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. I: D(3K) series on characteristics 2,” Algebra Analiz, 16, No. 6, 53–122 (2004).
A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. II. Local algebras,” Zap Nauchn. Semin. POMI, 375, 92–129 (2010).
A. I. Generalov, “Hochschild cohomology of algebras of dihedral type. III. Local algebras in characteristics 2,” Vestnik SPb Univ., Ser. 1, Mat., Mekh., Astron., No. 1, 28–38 (2010).
A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. I: Generalized quaternion groups,” Algebra Analiz, 18, No. 1, 55–107 (2006).
A. I. Generalov, A. A. Ivanov, and S. O. Ivanov, “Hochschild cohomology of algebras of quaternion type. II. The family Q(2B)1 in characteristics 2,” Zap. Nauchn. Semin. POMI, 349, 53–134 (2007).
A. I. Generalov, “Hochschild cohomology of algebras of quaternion type. III. Algebras with a samll parameter,” Zap. Nauchn. Semin. POMI, 356, 46–84 (2008).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. I. Group algebras of semidihedral groups,” Algebra Analiz, 21, No. 2, 1–51 (2009).
A. I. Generalov, “Hochschild cohomology of algebras of semidihedral type. II. Local algebras,” Zap. Nauchn. Semin. POMI, 386, 144–202 (2011).
A. I. Generalov, “Hochschild cohomology of the integral group ring of the dihedral group. I. Even case,” Algebra Analiz, 19, No. 5, 70–123 (2007).
Yu. V. Volkov and A. I. Generalov, “Hochschild cohomology of self-injective algebras of tree type D n . I,” Zap. Nauchn. Semin. POMI, 343, 121–182 (2007).
Yu. V. Volkov, “Hochschild cohomology of self-injective algebras of tree type D n . II,” Zap. Nauchn. Semin. POMI, 365, 63–121 (2009).
Yu. V. Volkov and A. I. Generalov, “Hochschild cohomology of self-injective algebras of tree type D n . III,” Zap. Nauchn. Semin. POMI, 386, 100–128 (2011).
A. I. Generalov and N. Yu. Kosovskaya, “Hochschild cohomology of the Liu-Schulz algebras,” Algebra Analiz, 18, No. 4, 39–82 (2006).
Y. Xu and H. Xiang, “Hochschild cohomology rings of d-Koszul algebras,” J. Pure Applied Algebra, 215, 1–12 (2011).
K. Erdmann and S. Schroll, “On the Hochschild cohomology of tame Hecke algebras,” Arch. Math., 94, 117–127 (2010).
N. Snashall and R. Taillefer, “The Hochschild cohomology ring of a class of special biserial algebras,” J. Algebra Appl., 9, 73–122 (2010).
N. Snashall and R. Taillefer, “Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras,” Colloq. Math., 199, 79–93 (2010).
S. Schroll and N. Snashall, “Hochschild cohomology and support varieties for tame Hecke algebras,” Quart. J Math., to appear.
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 (2005).
K. Erdmann, T. Holm, and N. Snashall, “Twisted bimodules and Hochschild cohomology for self-injective algebras of class A n . II,” Algebras Repr. Theory, 5, 457–482 (2002).
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Translated Zapiski Nauchnykh Seminarov POMI, Vol. 388, 2011, pp. 210–246.
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Pustovykh, M.A. The Hochschild cohomology ring of Möbius algebras. J Math Sci 183, 692–714 (2012). https://doi.org/10.1007/s10958-012-0834-z
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DOI: https://doi.org/10.1007/s10958-012-0834-z