摘要
为了探讨代数的Cartan矩阵的某些性质与代数分类的关系,通过研究完全域k上的0型仿射箭图的一个有限维表示的自同态代数的结构与Jordan标准型的关系,并利用Jordan标准型的组合信息得到了该自同态代数的Cartan矩阵,验证了Cartan矩阵猜想在此情形下不成立.最后提出了一个有关仿射箭图性质的猜想.
In order to study the relationship of some properties of Cartan matrices of various algebras with the classifications of the algebras, by investigating the structure of the endomorphism algebra of a finite dimensional representation of quivers of type A0 over a perfect field k and using the combinatorial information of the Jordan canonical form of matrices, the Cartan matrix of the algebra is obtained and the Cartan matrix conjecture is proved to be not true in this case. A conjecture of some properties of affine quivers is presented in the end.
出处
《纯粹数学与应用数学》
CSCD
2010年第5期844-849,共6页
Pure and Applied Mathematics
基金
湖北师范学院研究生启动项目(2007D56)
