On Additive K-Theory with the Loday - Quillen *-Product - Kuribayashi, Katsuhiko; Yamaguchi, Toshihiro (MATHEMATICA SCANDINAVICA, 2000)
The *-product defined by Loday and Quillen [17] on the additive 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 K-theory K_*^+(Ω) for a differential graded algebra (Ω,d) over a commutative ring. We prove that Connes’ B-maps from the additive K-theory K_*^+(Ω) to the negative cyclic homology HC_*^-(Ω) and to the Hochschild homology HH_*(Ω) are morphisms of algebras under the *-product on K_*^+(Ω). Applications to topology of Connes’ B-maps are also described.