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

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)
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