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．
Let A be the algebra defined 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 A^op. Specially, 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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2006年第2期347-352,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10371101)
