Approach to artinian algebras via natural quivers

Fang Li Zhejiang University Zongzhu Lin Kansas State Univesity

Rings and Algebras mathscidoc:1702.31001

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY , 364, (3), 17, 2012.3
Given an Artinian algebra $A$ over a field $k$, there are several combinatorial objects associated to $A$. They are the diagram $D_A$ as defined by Drozd and Kirichenko, the natural quiver $\Delta_A$ defined by Li (cf. Section 2), and a generalized version of $k$-species $(A/r, r/r^2)$ with $r$ being the Jacobson radical of $A$. When $A$ is splitting over the field $k$, the diagram $D_A$ and the well-known ext-quiver $\Gamma_A$ are the same. The main objective of this paper is to investigate the relations among these combinatorial objects and in turn to use these relations to give a characterization of the algebra $A$.
Artinian algebra; natural quiver; generalized path algebra
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@inproceedings{fang2012approach,
  title={APPROACH TO ARTINIAN ALGEBRAS VIA NATURAL QUIVERS },
  author={Fang Li, and Zongzhu Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209094915495555367},
  booktitle={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY },
  volume={364},
  number={3},
  pages={17},
  year={2012},
}
Fang Li, and Zongzhu Lin. APPROACH TO ARTINIAN ALGEBRAS VIA NATURAL QUIVERS . 2012. Vol. 364. In TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY . pp.17. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209094915495555367.
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