Proceedings of the American Mathematical Society

Author(s): Andrea Solotar; Micheline Vigué-Poirrier
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 16E40, 16W50
Posted: November 2, 2009
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Abstract: We prove without any assumption on the ground field that higher Hochschild homology groups do not vanish for two large classes of algebras whose global dimension is not finite.

1.: Avramov, L.; Vigué-Poirrier, M. Hochschild homology criteria for smoothness. Internat. Math. Res. Notices 1 (1992), 17-25. MR 1149001 (92m:13020)
2.: Bavula, V. V. Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras, Bull. Sci. Math. 120 (1996), no. 3, 293-335. MR 1399845 (97f:16015)
3.: Bergh, P. A.; Erdmann, K. Homology and cohomology of quantum complete intersections. Algebra Number Theory 2 (2008), no. 5, 501-522. MR 2429451 (2009h:16010)
4.: Bergh, P. A.; Madsen, D. Hochschild homology and global dimension. Bull. London Math. Soc. 41 (2009), no. 3, 473-482. MR 2506831
5.: Buchweitz, R.; Green, E.; Madsen, D.; Solberg, Ø. Finite Hochschild cohomology without finite global dimension. Math. Res. Lett. 12 (2005), 805-816. MR 2189240 (2006k:16019)
6.: Buenos Aires Cyclic Homology Group. Cyclic homology of algebras with one generator. (J. A. Guccione, J. J. Guccione, M. J. Redondo, A. Solotar and O. Villamayor participated in this research.) -Theory 5 (1991), 51-69. MR 1141335 (93b:19002)
7.: Félix, Y.; Halperin, S.; Thomas, J.-C. Differential graded algebras in topology. Handbook of algebraic topology, 829-865, North-Holland, Amsterdam, 1995. MR 1361901 (96j:57052)
8.: Félix, Y.; Halperin, S.; Thomas, J.-C. Rational homotopy theory. Graduate Texts in Mathematics, vol. 205, Springer-Verlag, New York, 2001. MR 1802847 (2002d:55014)
9.: Félix, Y.; Thomas, J.-C.; Vigué-Poirrier, M. The Hochschild cohomology of a closed manifold. Publ. Math. Inst. Hautes Études Sci. 99 (2004), 235-252. MR 2075886 (2005g:57054)
10.: Halperin, S.; Vigué-Poirrier, M. The homology of a free loop space. Pacific J. Math. 147 (1991), no. 2, 311-324. MR 1084712 (92e:55012)
11.: Han, Y. Hochschild (co)homology dimension. J. London Math. Soc. (2) 73 (2006), no. 3, 657-668. MR 2241972 (2007c:16018)
12.: Happel, D. Hochschild cohomology of finite-dimensional algebras. Séminaire d'Algèbre Paul Dubreil et Marie-Paul Malliavin, 39ème Année (Paris, 1987/1988), 108-126, Lecture Notes in Math., 1404, Springer, Berlin, 1989. MR 1035222 (91b:16012)
13.: Loday, J.-L. Cyclic homology. Appendix E by M. Ronco. Second edition. Chapter 13 by the author in collaboration with Teimuraz Pirashvili. Grundlehren der Mathematischen Wissenschaften, vol. 301, Springer-Verlag, Berlin, 1998. MR 1600246 (98h:16014)
14.: MacLane, S. Homology. Reprint of the first edition. Die Grundlehren der Mathematischen Wissenschaften, vol. 114, Springer-Verlag, Berlin-New York, 1967. MR 0349792 (50:2285)
15.: Serre, J.-P. Algèbre locale. Multiplicités. Lecture Notes in Math., 11, Springer-Verlag, Berlin, 1965. MR 0201468 (34:1352)
16.: Solotar, A. Cyclic homology of a free loop space. Comm. Algebra 21 (1993), no. 2, 575-582. MR 1199690 (94h:19003)
17.: Vigué-Poirrier, M. Homologie de Hochschild et homologie cyclique des algèbres différentielles graduées. International Conference on Homotopy Theory (Marseille-Luminy, 1988). Astérisque, vol. 191, Soc. Math. France, 1990, pp. 255-267. MR 1098974 (92e:19003)
18.: Vigué-Poirrier, M. Critères de nullité pour l'homologie des algèbres graduées. C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 7, 647-649. MR 1245091 (94g:19003)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16E40, 16W50

Andrea Solotar
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1 1428, Buenos Aires, Argentina
Email: asolotar@dm.uba.ar

Micheline Vigué-Poirrier
Affiliation: Laboratoire Analyse, Géométrie et Applications, UMR CNRS 7539, Institut Galilée, Université Paris 13, F-93430 Villetaneuse, France
Email: vigue@math.univ-paris13.fr

DOI: 10.1090/S0002-9939-09-10168-5
PII: S 0002-9939(09)10168-5
Keywords: Global dimension, Hochschild homology theory
Received by editor(s): June 12, 2009,
Received by editor(s) in revised form: August 16, 2009
Posted: November 2, 2009
Additional Notes: This work was supported by the projects UBACYTX212 and PIP-CONICET 5099. The first author is a research member of CONICET (Argentina) and a Regular Associate of ICTP Associate Scheme.
The second author is a research member of University of Paris 13, CNRS, UMR 7539 (LAGA)
Communicated by: Martin Lorenz
Copyright of article: Copyright 2009, American Mathematical Society

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