The Golbal Dimension And κ₀Group Of ω-SMASH Coproducts

This paper mainly studies the spectral sequence and the global dimension of ω-smash coproducts and characterizes its κ0group structures.This paper consists of the following three chapters.In chapter1, we introduce the research background and present the main results in this paper, and recall some basic concepts and useful properties related to R-smash products and w-smash coproducts.In chapter2, we construct the cotensor product over the coalgebra C by Cω(?)H comodules, where Cω(?)H denotes the w-smash coproduct. Consequently, we can prove that there exists a third quadrant spectral sequence. As an important application, we get the relation of global dimension among w-smash coproduct Cω(?)H, coalgebra C and Hopf algebra H.In chapter3, we mainly give show the Ko group structures of a R-smash product and the κ0group structures of a ω-smash coproduct, respectively. And, we prove that the κ0group of the w-smash coproduct is isomorphic to κ0group of the R-smash product.