偏缠绕模的Maschke型定理

A Maschke Type Theorem of Partial Entwined Modules

设(A,C,ψ),(A′,C′,ψ′)为两偏缠绕结构,给定α:A→A′和γ:C→C′.引入两个偏缠绕模范畴M(ψ)_A^C和M(ψ′)_A′~C′的导出函子F,并证明此导出函子F有右伴随函子:G:M(ψ′)_A′~C′→M(ψ)_A^C.最后,引入偏正规化余积分θ:C→AA的概念并证明了偏缠绕模范畴的Maschke型定理,也就是说,假设存在偏正规化余积分,给定M_A^C(ψ)中态射f:M→N,则有当单(满)态射f看作C-余模态射可分裂时,必有单(满)态射f在M_A^C(ψ)中可分裂.

Let（A,C,ψ）,（A′,C′,ψ′）be two partial entwining structures.Givenα：A→A′andγ：C→C′,we define an induction functor Fbetween the category M（ψ′）_AC of all partial entwined modules and the category M（ψ′）_A′C′,and we prove that this functor has a right adjoint G：M（ψ′）_A′C′ →M（ψ）_AC.Finally,we introduce the definition of partial conormalized cointegral θ：C→AAand prove a Maschke type theorem for the category of partial entwined modules,that is,suppose that there exists a partial normalized cointegral.Then f：M→Nin M_AC（ψ）has a section（respectively,retraction）if fhas a section（respectively,retraction）as a C-comodule morphism.