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
Hochschild, G., On the cohomology groups of an associative algebra, Annals of Math. 46 (1945), 58–67.
Hochschild, G., Relative homological algebra, Trans. Ams 82 (1956), 246–269
Lipman, J., Residues and traces of differential forms via Hochschild homology, Contemporary Mathematics 611987.
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
McCarthy, R., L’équivalence de Morita et l’homologie cyclique, C. R. Acad. Sci. Paris Sér. A-B 307 (1988), 211–215
Brylinski, J.-L., Central localization in Hochschild homology, J. Pure Applied Alg. 57 (1989), 1–4
Geller, S., Weibel, C., Etale descent for Hochschild and cyclic homology, Com-ment. Math. Hely. 66 (1991), 368–388.
Kadison, L., A relative cyclic cohomology theory useful for computation, C. R. Acad. Sci. Paris Sér. A-B 308 (1989), 569–573
Wodzicki, M., Excision in cyclic homology and in rational algebraic K-theory, Ann. Math. 129 (1989), 591–639. 91h: 19008
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
Cibils, C., Cyclic and Hochschild homology of 2-nilpotent algebras, K-theory 4 (1990), 131–141
Koszul, J.L., Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France 78 (1950), 65–127
Hochschild, G., Kostant, B., Rosenberg, A., Differential forms on regular affine algebras, Trans. Ams 102 (1962), 383–408. 26# 167
Loday, J.-L., Homologies diédrale et quaternionique, Advances in Math. 66 (1987), 119–148. 89e: 18024
Wodzicki, M., Excision in cyclic homology and in rational algebraic K-theory, Ann. Math. 129 (1989), 591–639. 91h: 19008
Hochschild, G., On the cohomology groups of an associative algebra, Annals of Math. 46 (1945), 58–67.
Kassel, C., Loday, J.-L., Extensions centrales d’algèbres de Lie, Ann. Inst. Fourier 33 (1982), 119–142. 85g: 17004
Gerstenhaber, M., Schack, S.D., The shuffle bialgebra and the cohomology of commutative algebras, J. Pure Appl. Algebra 70 (1991), 263–272.
Gabriel, P., Zisman, M., Calculus of fractions and homotopy theory, Erg. Math., Springer, 1967.
May, J.P., Simplicial objects in algebraic topology, Van Nostrand, Princeton, 1967
Bousfield, A.K., Kan, D.M., Homotopy limits, completions and localizations, Springer Lect. Notes in Math. 304, 1972.
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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
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