## Homology, Homotopy and Applications

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

#### Abstract

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.

#### Article information

Source
Homology Homotopy Appl., Volume 4, Number 1 (2002), 191-212.

Dates
First available in Project Euclid: 13 February 2006

https://projecteuclid.org/euclid.hha/1139840061

Mathematical Reviews number (MathSciNet)
MR1983016

Zentralblatt MATH identifier
06826201

#### Citation

Kantorovitz, Miriam Ruth; McCarthy, Randy. The Taylor towers for rational algebraic $K$-theory and Hochschild homology. Homology Homotopy Appl. 4 (2002), no. 1, 191--212. https://projecteuclid.org/euclid.hha/1139840061