Abstract
relating cyclic and Hochschild homology, one can see that any formula for HC,(A @A’) will not only involve HC,(A) and HC,(A’), but also the “periodicity” operator S and the Hochschild groups. Fortunately, if the map S brings in some complications, it also endows HC,(A) with a comodule structure over the cyclic homology of the ground ring k. Actually, the comodule structure exists already on the complex level: a convenient complex on which S has the form of a canonical surjection is Connes’s double complex with differentials b and B. Now the idea is to view the cyclic homology of an algebra as a composite functor
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