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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Crossed simplicial groups and their associated homology
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by Zbigniew Fiedorowicz and Jean-Louis Loday PDF
Trans. Amer. Math. Soc. 326 (1991), 57-87 Request permission


We introduce a notion of crossed simplicial group, which generalizes Connes’ notion of the cyclic category. We show that this concept has several equivalent descriptions and give a complete classification of these structures. We also show how many of Connes’ results can be generalized and simplified in this framework.
    R. Aboughazi, Groupes simpliciaux croisés symétriques et hyperoctahédral, Preprint, IRMA, Strasbourg, 1986.
  • A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
  • Dan Burghelea, Cyclic homology and the algebraic $K$-theory of spaces. I, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 89–115. MR 862632, DOI 10.1090/conm/055.1/862632
  • Alain Connes, Cohomologie cyclique et foncteurs $\textrm {Ext}^n$, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 23, 953–958 (French, with English summary). MR 777584
  • W. G. Dwyer and D. M. Kan, Normalizing the cyclic modules of Connes, Comment. Math. Helv. 60 (1985), no. 4, 582–600. MR 826872, DOI 10.1007/BF02567433
  • F. Goichot, Homologie cyclique: produits, généralisations, Preprint, IRMA, Strasbourg, 1986.
  • Jean-Louis Loday, Homologies diédrale et quaternionique, Adv. in Math. 66 (1987), no. 2, 119–148 (French). MR 917736, DOI 10.1016/0001-8708(87)90032-6
  • Jean-Louis Loday and Daniel Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), no. 4, 569–591. MR 780077, DOI 10.1007/BF02566367
  • Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
  • Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129
  • M. S. Raghunathan, Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York-Heidelberg, 1972. MR 0507234
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 326 (1991), 57-87
  • MSC: Primary 18F25; Secondary 18D05, 19D55, 20F36, 55U10
  • DOI:
  • MathSciNet review: 998125