Cotorsion dimensions and FP-projective dimensions of weak Hopf actions

Abstract

Let H be a finite dimensional weak Hopf algebra and A be an H-module algebra. In this paper, we mainly discuss the relations of cotorsion dimension and FP-projective dimension between A\mathrm{♯}H and A. As applications, sufficient conditions are given for \mathrm{L}\mathrm{C}\mathrm{D}\left(A\mathrm{♯}H\right)=\mathrm{L}\mathrm{C}\mathrm{D}\left(A\right) and \mathrm{L}\mathrm{F}\mathrm{P}\mathrm{D}\left(A\mathrm{♯}H\right)=\mathrm{L}\mathrm{F}\mathrm{P}\mathrm{D}\left(A\right).

Keywords

Cotorsion dimension / FP-projective dimension / weak Hopf algebra

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