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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 614–623
DOI: https://doi.org/10.4213/mzm8985 (Mi mzm8985) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Cotorsion Dimensions and Hopf Algebra Actions

Xiuli Chen, Haiyan Zhu, Fang Li

Zhejiang University
Full-text PDF (470 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm8985
Abstract: 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, cotorsion dimension, smash product, projective dimension, Gorenstein dimension.
Received: 08.09.2010
Revised: 06.01.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 616–623
DOI: https://doi.org/10.1134/S0001434613030309
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: Russian
Citation: Xiuli Chen, Haiyan Zhu, Fang Li, “Cotorsion Dimensions and Hopf Algebra Actions”, Mat. Zametki, 93:4 (2013), 614–623; Math. Notes, 93:4 (2013), 616–623
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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