The Hochschild cohomology ring for one of the two series of self-injective algebras of tree class E6 is described in terms of generators and relations.
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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 A n ,” 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 D n . I,” Zap. Nauchn. Semin. POMI, 343, 121–182 (2007).
Yu. V. Volkov, “Hochschild cohomology for self-injective algebras of tree class D n . 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 D n . III,” Zap. Nauchn. Semin. POMI, 386, 100–128 (2011).
Yu. V. Volkov, “Hochschild cohomology for nonstandard self-injective algebras of tree class D n ,” Zap. Nauchn. Semin. POMI, 388, 48–99 (2011).
Yu. V. Volkov, “Hochschild cohomology for self-injective algebras of tree class D n . IV,” Zap. Nauchn. Semin. POMI, 388, 100–118 (2011).
Yu. V. Volkov, “Hochschild cohomology for self-injective algebras of tree class D n . V,” Zap. Nauchn. Semin. POMI, 394, 140–173 (2011).
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. Pustovykh, “Hochschild cohomology ring for self-injective algebras of tree class E 6,” http://arxiv.org/abs/1311.4756.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, pp. 205–243.
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Pustovykh, M.A. The Hochschild Cohomology Ring for Self-Injective Algebras of Tree Class E 6 . J Math Sci 209, 614–644 (2015). https://doi.org/10.1007/s10958-015-2517-z
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DOI: https://doi.org/10.1007/s10958-015-2517-z