A multiplication in cyclic homology
HTML articles powered by AMS MathViewer
- by Kiyoshi Igusa PDF
- Trans. Amer. Math. Soc. 352 (2000), 209-242 Request permission
Abstract:
We define a multiplication on the cyclic homology of a commutative, cocommutative bialgebra $H$ with “superproduct.” In the case when $H$ is a field of characteristic zero the cyclic homology becomes a polynomial algebra in one generator. (The Loday-Quillen multiplication is trivial in that case.)References
- Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176
- B. L. Feĭgin and B. L. Tsygan, Additive $K$-theory, $K$-theory, arithmetic and geometry (Moscow, 1984–1986) Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 67–209. MR 923136, DOI 10.1007/BFb0078368
- P. Gaucher, Opérations sur l’homologie d’algèbres de matrices et homologie cyclique, Ph.D. thesis, Universite Louis Pasteur, Strasbourg, France, 1992.
- Thomas G. Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985), no. 2, 187–215. MR 793184, DOI 10.1016/0040-9383(85)90055-2
- Dale Husemoller, Homology of certain $H$-spaces as group ring objects, Algebra, topology, and category theory (a collection of papers in honor of Samuel Eilenberg), Academic Press, New York, 1976, pp. 77–94. MR 0413101
- K. Igusa and J. Klein, The Borel regulator map on pictures II: an example from Morse theory, preprint.
- R. W. Thomason, Les $K$-groupes d’un schéma éclaté et une formule d’intersection excédentaire, Invent. Math. 112 (1993), no. 1, 195–215 (French). MR 1207482, DOI 10.1007/BF01232430
- John D. S. Jones, Cyclic homology and equivariant homology, Invent. Math. 87 (1987), no. 2, 403–423. MR 870737, DOI 10.1007/BF01389424
- Jean-Louis Loday, Opérations sur l’homologie cyclique des algèbres commutatives, Invent. Math. 96 (1989), no. 1, 205–230 (French). MR 981743, DOI 10.1007/BF01393976
- 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
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
- Friedhelm Waldhausen, Algebraic $K$-theory of spaces, Algebraic and geometric topology (New Brunswick, N.J., 1983) Lecture Notes in Math., vol. 1126, Springer, Berlin, 1985, pp. 318–419. MR 802796, DOI 10.1007/BFb0074449
Additional Information
- Kiyoshi Igusa
- Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254-9110
- MR Author ID: 90790
- ORCID: 0000-0003-2780-0924
- Received by editor(s): April 14, 1994
- Published electronically: September 8, 1999
- Additional Notes: This research was supported by NSF grant no. DMS 90 02512
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 209-242
- MSC (1991): Primary 18G60; Secondary 16W30
- DOI: https://doi.org/10.1090/S0002-9947-99-02447-2
- MathSciNet review: 1650093