Geodesic
The harmonic decomposition in cyclic homology
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 6, pp. 165-170.

Voir la notice de l'article provenant de la source Math-Net.Ru

It has been shown by Cuntz and Quillen that in characteristic $0$ the kernel of the square of the “noncommutative Laplacian” on the Hochschild and cyclic complexes contains the relevant homology information. In this note, we show that the same property holds for the plain kernel of this Laplacian, as in differential geometry. Using the same ideas, we define a variant of Hochschild homology and cyclic homology and show that we recover the classical definitions in characteristic $0$. 
@article{FPM_2016_21_6_a6,
     author = {M. Karoubi},
     title = {The harmonic decomposition in cyclic homology},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {165--170},
     publisher = {mathdoc},
     volume = {21},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a6/}
}
TY  - JOUR
AU  - M. Karoubi
TI  - The harmonic decomposition in cyclic homology
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2016
SP  - 165
EP  - 170
VL  - 21
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a6/
LA  - ru
ID  - FPM_2016_21_6_a6
ER  - 
%0 Journal Article
%A M. Karoubi
%T The harmonic decomposition in cyclic homology
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2016
%P 165-170
%V 21
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a6/
%G ru
%F FPM_2016_21_6_a6
M. Karoubi. The harmonic decomposition in cyclic homology. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 6, pp. 165-170. http://geodesic.mathdoc.fr/item/FPM_2016_21_6_a6/

[1] Connes A., “Noncommutative differential geometry”, Publ. Math. IHES, 62, 1985, 257–360 | DOI | MR

[2] Cuntz J., Quillen D., “Operators on noncommutative differential forms and cyclic homology”, Geometry, Topology and Physics, International Press, Cambridge, 1995, 77–111 | MR | Zbl

[3] Karoubi M., Homologie cyclique et K-théorie, Astérisque, 149, Soc. Math. de France, 1987 | MR

[4] Kassel C., “Cyclic homology, comodules and mixed complexes”, J. Algebra, 107 (1987), 195–216 | DOI | MR | Zbl

[5] Loday J.-L., Quillen D., “Cyclic homology and the Lie algebra homology of matrices”, Comment. Math. Helvetici, 59 (1984), 565–591 | DOI | MR | Zbl