Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of ...Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra ? of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.展开更多
基金the National Natural Science Foundation of China (Grant No.10671016)the 985 Project of Beijing Normal University
文摘Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra ? of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.
