Approach to Artinian algebras via natural quivers
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- by Fang Li and Zongzhu Lin
- Trans. Amer. Math. Soc. 364 (2012), 1395-1411
- DOI: https://doi.org/10.1090/S0002-9947-2011-05410-3
- Published electronically: November 7, 2011
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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 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 $A$.References
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Bibliographic Information
- Fang Li
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China
- Email: fangli@cms.zju.edu.cn
- Zongzhu Lin
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- MR Author ID: 214053
- Email: zlin@math.ksu.edu
- Received by editor(s): August 14, 2009
- Received by editor(s) in revised form: May 18, 2010
- Published electronically: November 7, 2011
- Additional Notes: This project was supported by the National Natural Science Foundation of China (No. 10871170) and the Natural Science Foundation of Zhejiang Province of China (No. D7080064)
The second author was supported in part by an NSA grant and the NSF I/RD program - © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 1395-1411
- MSC (2010): Primary 16G10, 16G20; Secondary 16P20, 13E10
- DOI: https://doi.org/10.1090/S0002-9947-2011-05410-3
- MathSciNet review: 2869180