Homology, Homotopy and Applications

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

Miriam Ruth Kantorovitz and Randy McCarthy

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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


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