A Chern character in cyclic homology

Zamboni, Luca Quardo

doi:10.1090/S0002-9947-1992-1044967-X

A Chern character in cyclic homology
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by Luca Quardo Zamboni

Trans. Amer. Math. Soc. 331 (1992), 157-163

DOI: https://doi.org/10.1090/S0002-9947-1992-1044967-X

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Abstract:

We show that inner derivations act trivially on the cyclic cohomology of the normalized cyclic complex $\mathcal {C}(\Omega )/\mathcal {D}(\Omega )$ where $\Omega$ is a differential graded algebra. This is then used to establish the fact that the map introduced in $[ \text {GJ} ]$ defines a Chern character in $K$ theory.

References

Kuo-tsai Chen, Iterated integrals of differential forms and loop space homology, Ann. of Math. (2) 97 (1973), 217–246. MR 380859, DOI 10.2307/1970846
Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176
Ezra Getzler and John D. S. Jones, $A_\infty$-algebras and the cyclic bar complex, Illinois J. Math. 34 (1990), no. 2, 256–283. MR 1046565
Ezra Getzler, John D. S. Jones, and Scott Petrack, Differential forms on loop spaces and the cyclic bar complex, Topology 30 (1991), no. 3, 339–371. MR 1113683, DOI 10.1016/0040-9383(91)90019-Z
John D. S. Jones, Cyclic homology and equivariant homology, Invent. Math. 87 (1987), no. 2, 403–423. MR 870737, DOI 10.1007/BF01389424
Christian Kassel, L’homologie cyclique des algèbres enveloppantes, Invent. Math. 91 (1988), no. 2, 221–251 (French, with English summary). MR 922799, DOI 10.1007/BF01389366
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
B. L. Tsygan, Homology of matrix Lie algebras over rings and the Hochschild homology, Uspekhi Mat. Nauk 38 (1983), no. 2(230), 217–218 (Russian). MR 695483