Opérations sur l'homologie cyclique des algèbres commutatives. (Operations on the cyclic homology of commutative algebras) (Q1262384)

Let Fin denote the category whose objects are the sets \([n]:=\{0,1,...,n\}\) and whose morphisms are arbitrary maps. Starting from the subcategory of order preserving maps, classically one has derived many (co)homology theories in topology and algebra, namely all those which can be defined by semi-simplicial methods. If one adds cyclic maps [n]\(\to [n]\), one derives the so called cyclic homology. Elements of \(S_{n+1}\), the symmetric group, operate on Fin([m],[n]) and Fin([n],[m]). Therefore special elements of the group ring \({\mathbb{Z}}[S_ n]\), called eulerian elements, give rise to oprations on semisimplicial and cyclic homology groups, hence to canonical filtrations or even splittings of these groups. This is the theme of the paper.