Some algebraic properties of cyclic homology groups (Q1097959)

By its periodicity the cyclic cohomology HC *(A) of an associative algebra A over a commutative ring K becomes a module over the polynomial ring K[X] [\textit{J. D. S. Jones}: Cyclic homology and equivariant homology, Invent. Math. 87, 403-424 (1987)]. \(HC\) \(-_*(A)\) denotes the homology theory dual over K[X] which is different from the K[X]-module \(HC_*(A)\). Both HC *(A) and \(HC_*(A)\) are expressed in terms of \(HC\) \(-_*(A)\). Then, K[X] bilinear products and coproducts are constructed and systematically studied. Finally, the authors prove various Künneth theorems and gain a product preserving Chern character \(K_*(A)\to HC\) \(-_*(A)\), where \(K_*(A)\) is the algebraic K-theory of A.