On the McKay Quivers and $m$-Cartan Matrices

Guo Jinyun

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On the McKay Quivers and $m$-Cartan Matrices

Guo Jinyun * #

School of Mathematics and Computational Sciences, Xiangtan University

*Correspondence author

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Funding: 国家自然科学基金,教育部博士点基金（No.10671061,200505042004）

Opened online:27 November 2008

Accepted by: none

Citation: Guo Jinyun.On the McKay Quivers and $m$-Cartan Matrices[OL]. [27 November 2008] http://en.paper.edu.cn/en_releasepaper/content/26134

In this paper, we introduce $m$-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean, such as it is positive semi-definite, can be generalized to $m$-Cartan matrix of a McKay quiver. We also describe the McKay quiver for a finite abelian subgroup of a special linear group.

Keywords:McKay quiver;$m$-Cartan matrix;linear group;finite abelian group

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