Hokkaido Mathematical Journal

A note on skew group categories

Zhenqiang ZHOU

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Abstract

Let $G$ be a finite group, and $\mathscr{C}$ a $G$-abelian category. We prove that the skew group category $\mathscr{C}(G)$ is an abelian category under the condition that the order $|G|$ is invertible in $\mathscr{C}$. When the order $|G|$ is not invertible in $\mathscr{C}$, an example is given to show that $\mathscr{C}(G)$ is not an abelian category.

Article information

Source
Hokkaido Math. J., Volume 46, Number 2 (2017), 189-207.

Dates
First available in Project Euclid: 30 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1498788017

Digital Object Identifier
doi:10.14492/hokmj/1498788017

Mathematical Reviews number (MathSciNet)
MR3677880

Zentralblatt MATH identifier
1374.18019

Subjects
Primary: 18E10: Exact categories, abelian categories 16B50: Category-theoretic methods and results (except as in 16D90) [See also 18-XX]

Keywords
$G$-abelian category skew group category idempotent completion

Citation

ZHOU, Zhenqiang. A note on skew group categories. Hokkaido Math. J. 46 (2017), no. 2, 189--207. doi:10.14492/hokmj/1498788017. https://projecteuclid.org/euclid.hokmj/1498788017


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