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Hochschild Homology

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Cyclic Homology

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 301))

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Abstract

Since cyclic homology is, in a certain sense, a variant of Hochschild homology we begin with a chapter on this theory. Most of the material presented here is classical and has been known for more than thirty years (except Sect. 1.4). However our presentation is adapted to fit in with the subsequent chapters.

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Bibliographical Comments on Chapter 1

  • Bourbaki, N., Algèbre homologique, Algèbre chap. X, Masson, 1980

    MATH  Google Scholar 

  • Hochschild, G., On the cohomology groups of an associative algebra, Annals of Math. 46 (1945), 58–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Hochschild, G., Relative homological algebra, Trans. Ams 82 (1956), 246–269

    Article  MathSciNet  MATH  Google Scholar 

  • Lipman, J., Residues and traces of differential forms via Hochschild homology, Contemporary Mathematics 611987.

    Google Scholar 

  • Dennis, K., In search of a new homology theory, manuscript, 1976, never published. Dennis, K., Igusa, K., Hochschild homology and the second obstruction for pseudo-isotopy, Springer Lect. Notes in Math. 966 (1982), 7–58. 84m: 18014

    MathSciNet  Google Scholar 

  • McCarthy, R., L’équivalence de Morita et l’homologie cyclique, C. R. Acad. Sci. Paris Sér. A-B 307 (1988), 211–215

    MATH  Google Scholar 

  • Brylinski, J.-L., Central localization in Hochschild homology, J. Pure Applied Alg. 57 (1989), 1–4

    Article  MathSciNet  MATH  Google Scholar 

  • Geller, S., Weibel, C., Etale descent for Hochschild and cyclic homology, Com-ment. Math. Hely. 66 (1991), 368–388.

    MathSciNet  MATH  Google Scholar 

  • Kadison, L., A relative cyclic cohomology theory useful for computation, C. R. Acad. Sci. Paris Sér. A-B 308 (1989), 569–573

    MathSciNet  MATH  Google Scholar 

  • Wodzicki, M., Excision in cyclic homology and in rational algebraic K-theory, Ann. Math. 129 (1989), 591–639. 91h: 19008

    MathSciNet  Google Scholar 

  • Calvo, A., Homologie de Hochschild et homologie cyclique de certaines algèbres de matrices triangulaires, C. R. Acad. Sci. Paris Sér. A-B 306 (1988), 103–105

    MathSciNet  MATH  Google Scholar 

  • Cibils, C., Cyclic and Hochschild homology of 2-nilpotent algebras, K-theory 4 (1990), 131–141

    Article  MathSciNet  MATH  Google Scholar 

  • Koszul, J.L., Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France 78 (1950), 65–127

    MathSciNet  MATH  Google Scholar 

  • Hochschild, G., Kostant, B., Rosenberg, A., Differential forms on regular affine algebras, Trans. Ams 102 (1962), 383–408. 26# 167

    Google Scholar 

  • Loday, J.-L., Homologies diédrale et quaternionique, Advances in Math. 66 (1987), 119–148. 89e: 18024

    MathSciNet  Google Scholar 

  • Wodzicki, M., Excision in cyclic homology and in rational algebraic K-theory, Ann. Math. 129 (1989), 591–639. 91h: 19008

    MathSciNet  Google Scholar 

  • Hochschild, G., On the cohomology groups of an associative algebra, Annals of Math. 46 (1945), 58–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Kassel, C., Loday, J.-L., Extensions centrales d’algèbres de Lie, Ann. Inst. Fourier 33 (1982), 119–142. 85g: 17004

    Article  MathSciNet  Google Scholar 

  • Gerstenhaber, M., Schack, S.D., The shuffle bialgebra and the cohomology of commutative algebras, J. Pure Appl. Algebra 70 (1991), 263–272.

    Article  MathSciNet  MATH  Google Scholar 

  • Gabriel, P., Zisman, M., Calculus of fractions and homotopy theory, Erg. Math., Springer, 1967.

    Google Scholar 

  • May, J.P., Simplicial objects in algebraic topology, Van Nostrand, Princeton, 1967

    Google Scholar 

  • Bousfield, A.K., Kan, D.M., Homotopy limits, completions and localizations, Springer Lect. Notes in Math. 304, 1972.

    Google Scholar 

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© 1992 Springer-Verlag Berlin Heidelberg

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Loday, JL. (1992). Hochschild Homology. In: Cyclic Homology. Grundlehren der mathematischen Wissenschaften, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21739-9_1

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  • DOI: https://doi.org/10.1007/978-3-662-21739-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-21741-2

  • Online ISBN: 978-3-662-21739-9

  • eBook Packages: Springer Book Archive

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