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
Abstract:
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.References
-
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
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: https://doi.org/10.1090/S0002-9947-1991-0998125-4
- MathSciNet review: 998125