Geodesic
Cotorsion Dimensions and Hopf Algebra Actions
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 614-623.

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Let $H$ be a finite-dimensional Hopf algebra over a field $k$, and let $A$ be an $H$-module algebra. In this paper, we discuss the cotorsion dimension of the smash product $A\mathbin{\#}H$. We prove that $$ \mathrm{l.cot.D}(A\mathbin{\#}H) \leq \mathrm{l.cot.D}(A) + \mathrm{r.D}(H), $$ which generalizes the result of group rings. Moreover, we give some sufficient conditions for which $$ \mathrm{l.cot.D}(A\mathbin{\#}H) =\mathrm{l.cot.D}(A). $$ As applications, we study the invariants of IF properties and Gorenstein global dimensions.
Keywords: Hopf algebra, smash product, projective dimension, Gorenstein dimension.
Mots-clés : cotorsion dimension 
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Xiuli Chen; Haiyan Zhu; Fang Li. Cotorsion Dimensions and Hopf Algebra Actions. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 614-623. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a11/

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