考虑AsB的箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构和带关系箭图(Q′,I′)的自同构决定情况,证明了AsB的Frobenius态射由A的Frobenius态射和B的Frobenius态射决定;代数AsB的固定点代数同构于相应的代数A的固定点代数与B的固定点代数的张量积.
We consider the case when the quiver automorphism of the quiver(Q,I)is determined by the quiver automorphism of(Q,I)and(Q',I'),the following results are shown.The Frobenius morphism of AsB is determined by the Frobenius morphism of A and the Frobenius morphism of B;the fixed-point algebra of AsB is isomorphisic to the tensor of the fixed-point algebra of A and the fixed-point algebra of B.