Abstract

In this paper, 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 K. MSC 2010: 16T05, 18G20, 16W50

Highlights

  • The notion of color Hopf algebras first appeared in the book of Montgomery [6, 10.5.11]

  • Lorenz-Lorenz proved that the global dimension of a Hopf algebra is exactly the projective dimension of the trivial module K; see [5, Section 2.4]

  • Following Schauenburg [10] and Doi [3], we prove the fundamental theorem of color Hopf module

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Summary

Introduction

Lorenz-Lorenz proved that the global dimension of a Hopf algebra is exactly the projective dimension of the trivial module K; see [5, Section 2.4]. We show that the graded global dimension of a color Hopf algebra coincides with the graded projective dimension of the trivial module K, which is equal to the projective dimension of K. The paper is organized as follows: in Section 2, we provide some background material for color Hopf algebras.

Preliminaries
Graded global dimension of color Hopf algebras
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