TY - JOUR
AU - Kuribayashi, Katsuhiko
AU - Yamaguchi, Toshihiro
PY - 2000/09/01
Y2 - 2023/03/25
TI - On Additive K-Theory with the Loday - Quillen *-Product
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 87
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-14296
UR - https://www.mscand.dk/article/view/14296
SP - 5-21
AB - 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.
ER -