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arXiv · 1303.7049

Approach to artinian algebras via natural quivers

Fang Li·Zongzhu Lin
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Abstract

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 in [DK], the natural quiver $\Delta_A$ defined in \cite{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 $A$.

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Fang Li, Zongzhu Lin. 2013-03-28. Approach to artinian algebras via natural quivers. https://arxiv.org/abs/1303.7049

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