# On Additive K-Theory with the Loday - Quillen *-Product

## DOI:

https://doi.org/10.7146/math.scand.a-14296## Abstract

The $*$-product defined by Loday and Quillen [17] on the additive $\mathbf{K}$-theory (the cyclic homology with shifted degrees) $K_*^+(A)$ for a commutative ring $A$ is naturally extended to a product ($*$-product) on the additive $\mathbf{K}$-theory $K_*^+(\Omega)$ for a differential graded algebra $(\Omega,d)$ over a commutative ring. We prove that Connes' $\mathbf{B}$-maps from the additive $\mathbf{K}$-theory $K_*^+(\Omega)$ to the negative cyclic homology $\mathrm{HC}_*^-(\Omega)$ and to the Hochschild homology $\mathrm{HH}_*(\Omega)$ are morphisms of algebras under the $*$-product on $K_*^+(\Omega)$. Applications to topology of Connes' $\mathbf{B}$-maps are also described.## Downloads

## Published

2000-09-01

## How to Cite

*MATHEMATICA SCANDINAVICA*,

*87*(1), 5–21. https://doi.org/10.7146/math.scand.a-14296

## Issue

## Section

Articles