| 对偶扩张代数的Frobenius态射和固定点代数 |
| |
| 引用本文： | 陈健敏,林亚南.对偶扩张代数的Frobenius态射和固定点代数[J].数学学报,2006,49(2):347-352. |
| |
| 作者姓名： | 陈健敏 林亚南 |
| |
| 作者单位： | 厦门大学数学科学学院,厦门361005 |
| |
| 基金项目： | 国家自然科学基金资助项目（10371101）.作者感谢邓邦明教授的有益建议. |
| |
| 摘 要： | 设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．
|
| 关 键 词： | 对偶扩张 Frobenius态射 固定点代数 |
| 文章编号： | 0583-1431（2006）02-0347-06 |
| 收稿时间： | 2004-11-02 |
| 修稿时间： | 2004-11-022005-01-12 |
Probenius Morphisms and Fixed-Point Algebra of the Dual Extension Algebras |
| |
| Jian Min CHEN ,Ya Nan LIN.Probenius Morphisms and Fixed-Point Algebra of the Dual Extension Algebras[J].Acta Mathematica Sinica,2006,49(2):347-352. |
| |
| Authors: | Jian Min CHEN Ya Nan LIN |
| |
| Institution: | Department of Mathematics, Xiamen University, Xiamen 361005, P. R. China |
| |
| Abstract: | Let A be the algebra denned by a quiver Q and a relationship I, D(A) the dual extension of A. D(A) is defined by the the quiver Q* and relations I*. In this paper, the following results are shown. The quiver automorphism of the quiver (Q*,I*) is determined by the quiver automorphism of (Q, I); the Frobenius morphism of D(A) is determined by the Frobenius morphism of A; the fixed-point algebra of D(A) is isomorphisic to the tensor of the fixed-point algebra of A and the fixed-point algebra of Aop. Specialiy,in the case when Q is simple quiver, the fixed-point algebra of D(A) is isomorphisic to the dual extension of the fixed-point algebra of A. |
| |
| Keywords: | dual extension algebra Frobenius morphism fixed-point algebra |
| 本文献已被 CNKI 维普 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
|
