扩张代数A_sB的Frobenius态射和固定点代数

Frobenius morphism and fixed-point algebra of the extension algebra A_sB

考虑AsB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AsB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 AsB is determined by the Frobenius morphism of A and the Frobenius morphism of B;the fixed-point algebra of AsB is isomorphisic to the tensor of the fixed-point algebra of A and the fixed-point algebra of B.