| Hopf algebraic theory has important applications in many mathematical fields,such as algebraic topology,group theory,quantum group and so on.In 1999,Moerdi-jk constructed a family of Hopf P-algebras through the initial P[λ]-algebra in which P is a given Hopf operad.In particular,Connes-Kreimer Hopf algebra is one of this family of Hopf P-algebras.In 2004,Laan,inspired by Moerdijk,constructed a fam-ily of Hopf P-algebras through the initial P[λn]-algebra in which P is a given Hopf operad.This family of Hopf P-algebras contains n-edge-colored Connes-Kreimer Hopf algebras.Based on the research of Moerdijk and Laan,this paper constructs a more extensive family of Hopf P-algebras through the initial P[(λω,n)ω∈Ω]-algebra,and further generalizes the study of Moerdijk and Laan:the conclusion of Laan can be obtained by taking |Ω|=1,and the conclusion of Moerdijk can be obtained by taken n=1 and |Ω|=1.Specifically,as an application,a family of Hopf algebras on the n-edge dyed root trees with dot decoration are constructed. |
