# The Taylor towers for rational algebraic K-theory and Hochschild homology

## Miriam Ruth Kantorovitz and Randy McCarthy

We compute the Taylor tower for Hochschild homology as a functor from augmented commutative simplicial \$\dbQ\$-algebras, to chain complexes over \$\dbQ\$. We use this computation to obtain the layers for the Taylor tower of rational algebraic \$K\$-theory. We also show that the Hodge decomposition for rational Hochschild homology is the decomposition of the Taylor tower of the augmentation ideal functor into its homogeneous layers when evaluated at a suspension.

Homology, Homotopy and Applications, Vol. 4(2002), No. 1, pp. 191-212

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