Homological algebra/Functional analysis
The cyclic homology of crossed-product algebras, I
[L'homologie cyclique des algèbres produits-croisés, I]
Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 618-622.

Dans cette note, on donne des quasi-isomorphismes explicites calculant l'homologie cyclique des algèbres produits-croisés.

In this note we produce explicit quasi-isomorphisms computing the cyclic homology of crossed-product algebras.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.04.012
Ponge, Raphaël 1

1 Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea
@article{CRMATH_2017__355_6_618_0,
     author = {Ponge, Rapha\"el},
     title = {The cyclic homology of crossed-product algebras, {I}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {618--622},
     publisher = {Elsevier},
     volume = {355},
     number = {6},
     year = {2017},
     doi = {10.1016/j.crma.2017.04.012},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.04.012/}
}
TY  - JOUR
AU  - Ponge, Raphaël
TI  - The cyclic homology of crossed-product algebras, I
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 618
EP  - 622
VL  - 355
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.04.012/
DO  - 10.1016/j.crma.2017.04.012
LA  - en
ID  - CRMATH_2017__355_6_618_0
ER  - 
%0 Journal Article
%A Ponge, Raphaël
%T The cyclic homology of crossed-product algebras, I
%J Comptes Rendus. Mathématique
%D 2017
%P 618-622
%V 355
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.04.012/
%R 10.1016/j.crma.2017.04.012
%G en
%F CRMATH_2017__355_6_618_0
Ponge, Raphaël. The cyclic homology of crossed-product algebras, I. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 618-622. doi : 10.1016/j.crma.2017.04.012. http://www.numdam.org/articles/10.1016/j.crma.2017.04.012/

[1] Baum, P.; Connes, A. Chern character for discrete groups, A Fête of Topology, Academic Press, Boston, 1988, pp. 163-232

[2] Brodzki, J.; Dave, S.; Nistor, V. The periodic cyclic homology of crossed products of finite type algebras, Adv. Math., Volume 306 (2017), pp. 494-523

[3] Brylinski, J.-L.; Nistor, V. Cyclic cohomology of étale groupoids, K-Theory, Volume 8 (1994), pp. 341-365

[4] Burghelea, D. The cyclic homology of the group rings, Comment. Math. Helv., Volume 60 (1985), pp. 354-365

[5] Connes, A. Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math., Volume 62 (1985), pp. 257-360

[6] Connes, A. Cyclic cohomology and the transverse fundamental class of a foliation, Pitman Research Notes in Mathematics, vol. 123, Longman, Harlow, 1986, pp. 52-144

[7] Connes, A. Noncommutative Geometry, Academic Press, San Diego, 1994

[8] Crainic, M. Cyclic cohomology of étale groupoids: the general case, K-Theory, Volume 17 (1999), pp. 319-362

[9] Emmanouil, I. On a class of groups satisfying Bass' conjecture, Invent. Math., Volume 132 (1998), pp. 307-330

[10] Feigin, B.; Tsygan, B. Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras, Lecture Notes in Math., vol. 1289, Springer, 1987, pp. 210-239

[11] Getzler, E.; Jones, J.D.S. The cyclic cohomology of crossed product algebras, J. Reine Angew. Math., Volume 445 (1993), pp. 161-174

[12] Ji, R. Nilpotency of Connes' periodicity operator and the idempotent conjectures, K-Theory, Volume 9 (1995), pp. 59-76

[13] Jones, J.D.S.; Kassel, C. Bivariant cyclic theory, K-Theory, Volume 3 (1989), pp. 339-365

[14] Kassel, C. Homologie cyclique, caractère de Chern et lemme de perturbation, J. Reine Angew. Math., Volume 408 (1990), pp. 159-180

[15] Loday, J.-L. Cyclic Homology, Springer, Berlin, 1992

[16] Marciniak, Z. Cyclic homology of group rings, Banach Center Publ., vol. 18, PWN, Warsaw, 1986, pp. 210-239

[17] Nistor, V. Group cohomology and the cyclic cohomology of crossed products, Invent. Math., Volume 99 (1990), pp. 411-424

[18] Ponge, R. The cyclic homology of crossed-product algebras, II, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017), pp. 623-627

[19] R. Ponge, Perturbation lemma, para-S-modules, and cup product for paracyclic modules, in preparation.

Cité par Sources :