An approach to operations on cyclic homology (Q1916146)

By operations on the cyclic homology of an algebra \(A\), the author means a Lie operation of the Hochschild cohomology of \(A\) on the bivariant cyclic cohomology of \(A\). His new and simple approach is based on the Cuntz-Quillen notion of an \(X\)-complex of coalgebras. Concerning these operations, see also [\textit{I. M. Gel'fand}, \textit{Yu. L. Daletskij} and \textit{B. L. Tsygan}, ``On a variant of noncommutative differential geometry'', Sov. Math. Dokl. 40, No. 2, 422-426 (1990; Zbl 0712.17026); translation from Dokl. Akad. Nauk SSSR 308, No. 6, 1293-1297 (1989)] and [\textit{E. Getzler}, ``Cartan homotopy formula and the Gauss-Manin connection in cyclic homology,'' Isr. Math. Conf. Proc. 7, 65-78 (1993; Zbl 0844.18007)].