## Homology, Homotopy and Applications

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

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

Miriam Ruth Kantorovitz and Randy McCarthy

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR1983016

**Zentralblatt MATH identifier**

06826201

**Subjects**

Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60]

Secondary: 16D40: Free, projective, and flat modules and ideals [See also 19A13] 55U35: Abstract and axiomatic homotopy theory

#### 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