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Mat. Zametki, 2013, Volume 93, Issue 4, Pages 614–623 (Mi mz8985)  

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

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.

DOI: https://doi.org/10.4213/mzm8985

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English version:
Mathematical Notes, 2013, 93:4, 616–623

Bibliographic databases:

Document Type: Article
UDC: 512.5
Received: 08.09.2010
Revised: 06.01.2011

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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\by Xiuli Chen, Haiyan Zhu, Fang Li
\paper Cotorsion Dimensions and Hopf Algebra Actions
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\yr 2013
\vol 93
\issue 4
\pages 614--623
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zhou X., Wei M., “Notes on cotorsion dimension of Hopf–Galois extensions”, Turk. J. Math., 40:1 (2016), 108–113  crossref  mathscinet  isi  scopus
  • Математические заметки Mathematical Notes
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