On the Steenrod operations in cyclic cohomology

Abstract

For a commutative Hopf algebra A over Z/p, where p is a prime integer, we define the Steenrod operations P i in cyclic cohomology of A using a tensor product of a free resolution of the symmetric group S n and the standard resolution of the algebra A over the cyclic category according to Loday (1992). We also compute some of these operations.

Steenrod operations on the negative cyclic homology of the shc-cochain algebras

“…2.1.6. Shc-equivalence and shc-formality [20,5] The shc cochain algebras (A, d A , µ A ) and (A , d A , µ A ) are said to be shc-equivalent (A shc A ) if there exists a sequence of shc morphisms A ← A 1 → • • • → A which are quasi-isomorphisms. One particular case of shc-equivalence is the shc-formality.…”