On graded global dimension of color Hopf algebras. (English) Zbl 1218.16023

Wang, Yan-Hua

J. Gen. Lie Theory Appl. 5, Article ID G110101, 6 p. (2011).

Summary: We prove the fundamental theorem of color Hopf module similar to the fundamental theorem of Hopf module. As an application, we prove that the graded global dimension of a color Hopf algebra coincides with the projective dimension of the trivial module \(\mathbb K\).

MSC:

16T05	Hopf algebras and their applications
16E10	Homological dimension in associative algebras
16W50	Graded rings and modules (associative rings and algebras)

Keywords:

color Hopf modules; graded global dimension; color Hopf algebras; projective dimension