@article{Kuribayashi_Yamaguchi_2000, title={On Additive K-Theory with the Loday - Quillen *-Product}, volume={87}, url={https://www.mscand.dk/article/view/14296}, DOI={10.7146/math.scand.a-14296}, abstractNote={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.}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Kuribayashi, Katsuhiko and Yamaguchi, Toshihiro}, year={2000}, month={Sep.}, pages={5–21} }