A decomposition for the cyclic cohomology of a commutative algebra (Q916980)

Let k be a fixed commutative unital \({\mathbb{Q}}\)-algebra and A be an associative k-algebra. For A commutative a Hodge-type decomposition of its cyclic cohomology \(H^ 0_{\lambda}(A)\) is presented (theorem 2). The periodicity sequence investigated in the second part is then applied to the particular case of the Fréchet algebra \(C^{\infty}({\mathcal K})\) of \(C^{\infty}\)-functions on a smooth compact manifold \({\mathcal K}\) (Connes' decomposition: theorem 8).