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The special issue of algebraic representation theory

Xueqing Chen, University of Wisconsin-Whitewater, USA chenx@uww.edu

Min Huang, Research Fellow, University of Hong Kong, China; Sun Yat-sen University (Zhuhai Campus), China minhuang1989@hotmail.com

Fang Li, Zhejiang University, China fangli@zju.edu.cn

Gorenstein global dimensions relative to balanced pairsSpecial Issues
Haiyu Liu, Rongmin Zhu and Yuxian Geng
2020, 28(4): 1563-1571 doi: 10.3934/era.2020082 +[Abstract](19)+[HTML](13) +[PDF](294.33KB)

Let \begin{document}$ \mathcal{G}(\mathcal{X}) $\end{document} and \begin{document}$ \mathcal{G}(\mathcal{Y}) $\end{document} be Gorenstein subcategories induced by an admissible balanced pair \begin{document}$ (\mathcal{X}, \mathcal{Y}) $\end{document} in an abelian category \begin{document}$ \mathcal{A} $\end{document}. In this paper, we establish Gorenstein homological dimensions in terms of these two subcategories and investigate the Gorenstein global dimensions of \begin{document}$ \mathcal{A} $\end{document} induced by the balanced pair \begin{document}$ (\mathcal{X}, \mathcal{Y}) $\end{document}. As a consequence, we give some new characterizations of pure global dimensions and Gorenstein global dimensions of a ring \begin{document}$ R $\end{document}.

On $ n $-slice algebras and related algebrasSpecial Issues
Jin-Yun Guo, Cong Xiao and Xiaojian Lu
2021, 29(4): 2687-2718 doi: 10.3934/era.2021009 +[Abstract](295)+[HTML](213) +[PDF](541.55KB)

The \begin{document}$ n $\end{document}-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of \begin{document}$ n $\end{document}-slice algebras via their \begin{document}$ (n+1) $\end{document}-preprojective algebras and the trivial extensions of their quadratic duals. One can always relate tame \begin{document}$ n $\end{document}-slice algebras to the McKay quiver of a finite subgroup of \begin{document}$ \mathrm{GL}(n+1, \mathbb C) $\end{document}. In the case of \begin{document}$ n = 2 $\end{document}, we describe the relations for the \begin{document}$ 2 $\end{document}-slice algebras related to the McKay quiver of finite Abelian subgroups of \begin{document}$ \mathrm{SL}(3, \mathbb C) $\end{document} and of the finite subgroups obtained from embedding \begin{document}$ \mathrm{SL}(2, \mathbb C) $\end{document} into \begin{document}$ \mathrm{SL}(3,\mathbb C) $\end{document}.

On inner Poisson structures of a quantum cluster algebra without coefficientsSpecial Issues
Fang Li and Jie Pan
2021, 29(5): 2959-2972 doi: 10.3934/era.2021021 +[Abstract](15)+[HTML](11) +[PDF](308.09KB)
Picture groups and maximal green sequencesSpecial Issues
Kiyoshi Igusa and Gordana Todorov
2021, 29(5): 3031-3068 doi: 10.3934/era.2021025 +[Abstract](15)+[HTML](11) +[PDF](534.52KB)

2020 Impact Factor: 1.833
5 Year Impact Factor: 1.833



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