Geodesic
Homotopy Formulas for Cyclic Groups Acting on Rings
Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 81-85

Voir la notice de l'article provenant de la source Cambridge University Press

The positive cohomology groups of a finite group acting on a ring vanish when the ring has a norm one element. In this note we give explicit homotopies on the level of cochains when the group is cyclic, which allows us to express any cocycle of a cyclic group as the coboundary of an explicit cochain. The formulas in this note are closely related to the effective problems considered in previous joint work with Eli Aljadeff.
DOI : 10.4153/CMB-2008-010-3
Mots-clés : 20J06, 20K01, 16W22, 18G35, group cohomology, norm map, cyclic group, homotopy 
Kassel, Christian. Homotopy Formulas for Cyclic Groups Acting on Rings. Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 81-85. doi: 10.4153/CMB-2008-010-3
@article{10_4153_CMB_2008_010_3,
     author = {Kassel, Christian},
     title = {Homotopy {Formulas} for {Cyclic} {Groups} {Acting} on {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {81--85},
     year = {2008},
     volume = {51},
     number = {1},
     doi = {10.4153/CMB-2008-010-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-010-3/}
}
TY  - JOUR
AU  - Kassel, Christian
TI  - Homotopy Formulas for Cyclic Groups Acting on Rings
JO  - Canadian mathematical bulletin
PY  - 2008
SP  - 81
EP  - 85
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-010-3/
DO  - 10.4153/CMB-2008-010-3
ID  - 10_4153_CMB_2008_010_3
ER  - 
%0 Journal Article
%A Kassel, Christian
%T Homotopy Formulas for Cyclic Groups Acting on Rings
%J Canadian mathematical bulletin
%D 2008
%P 81-85
%V 51
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-010-3/
%R 10.4153/CMB-2008-010-3
%F 10_4153_CMB_2008_010_3

[1] [1] Aljadeff, E. and Kassel, C., Explicit norm one elements for ring actions of finite abelian groups. Israel J. Math. 129(2002), 99–108. Google Scholar

[2] [2] Aljadeff, E. and Kassel, C., Norm formulas for finite groups and induction from elementary abelian subgroups. J. Algebra 303(2006), no. 2, 677–706. Google Scholar

[3] [3] Cartan, H. and Eilenberg, S., Homological Algebra. Princeton University Press, Princeton, 1956. Google Scholar

[4] [4] Kassel, C., Homologie cyclique, caractère de Chern et lemme de perturbation. J. Reine Angew. Math. 408(1990), 159–180. Google Scholar

Cité par Sources :