Hochschild cohomology of the Liu--Schulz algebras
Algebra i analiz, Tome 18 (2006) no. 4, pp. 39-82.

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A description of the Hochschild cohomology algebra for the symmetric 8-dimensional algebras found by Liu and Schulz is given in terms of generators and relations. The dimensions of the cohomology groups are calculated.
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A. I. Generalov; N. Yu. Kosovskaya. Hochschild cohomology of the Liu--Schulz algebras. Algebra i analiz, Tome 18 (2006) no. 4, pp. 39-82. http://geodesic.mathdoc.fr/item/AA_2006_18_4_a2/

[1] S. Eilenberg, S. MacLane, “Cohomology theory in abstract groups, I”, Ann. Math., 48 (1947), 51–78 | DOI | MR | Zbl

[2] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, M., 1960

[3] M. Gerstenhaber, “The cohomology structure of an associative ring”, Ann. Math., 78 (1963), 267–288 | DOI | MR | Zbl

[4] M. Gerstenhaber, S. D. Schack, “Algebraic cohomology and deformation theory”, Deformation theory of algebras and structures and applications, NATO ASI Ser., Ser. C: Math. and Phys. Sci., 247, eds. M. Hazewinkel, M. Gerstenhaber, Kluwer Acad. Publ., 1988, 11–264 | MR

[5] C. M. Ringel, “The Liu–Schulz example”, Representation theory of algebras, CMS Conf. Proc., 18, AMS, 1996, 587–600 | MR

[6] Sh. Liu, R. Schulz, “The existence of bounded infinite $DTr$-orbits”, Proc. Amer. Math. Soc., 122:4 (1994), 1003–1005 | DOI | MR | Zbl

[7] K. Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Math., 1428, Berlin, 1990 | MR | Zbl

[8] R. Schulz, “Boundedness and periodicity of modules over QF rings”, J. Algebra, 101:2 (1986), 450–469 | DOI | MR | Zbl

[9] E. S. Golod, “O koltse kogomologii konechnoi $p$-gruppy”, Dokl. Akad. nauk SSSR, 125:4 (1959), 703–706 | MR | Zbl

[10] B. B. Venkov, “Ob algebrakh kogomologii nekotorykh klassifitsiruyuschikh prostranstv”, Dokl. Akad. nauk SSSR, 127:5 (1959), 943–944 | MR | Zbl

[11] Evens L., “The cohomology ring of a finite group”, Trans. Amer. Math. Soc., 101 (1961), 224–239 | DOI | MR | Zbl

[12] A. I. Generalov, N. Yu. Fëdorova, “Algebra Ionedy dlya “primera Lyu–Shultsa””, Algebra i analiz, 14:4 (2002), 19–35 | MR | Zbl

[13] 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 | MR

[14] N. Yu. Kosovskaya, “Bimodulnaya rezolventa dlya algebr Lyu–Shultsa”, Zap. nauchn. semin. POMI, 321, 2005, 213–223 | MR | Zbl

[15] Th. Holm, “The Hochschild cohomology ring of a modular group algebra: the commutative case”, Commun. Algebra, 24 (1996), 1957–1969 | DOI | MR | Zbl

[16] C. Cibils, A. Solotar, “Hochschild cohomology algebra of abelian groups”, Arch. Math., 68 (1997), 17–21 | DOI | MR | Zbl