ABSTRACT
Let (H, A, C) be a threetuple, where H is a Hopf algebra coacting on an algebra A and acting on a coalgebra C, and C ℳ(H) A the category of representations of (H, A, C). Let z ∈ C ⊗ A be a generalized grouplike element of (H, A, C) and B the subalgebra of z-coinvariants of the Verma structure A ∈ C M(H) A . We prove the following affineness criterion: if there exist a total z-normalized integral γ: C → Hom(C, A) and if the canonical map β : A ⊗ B A → C ⊗ A , β ( a ⊗ B b ) = a ⋅ z ⋅ b https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187629/ac445a68-1635-4dfb-97a7-7653d5efb83a/content/inq_chapter12_215_1.tif"/> is surjective, then the induction functor − ⊗ B A : M B → C M ( H ) A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187629/ac445a68-1635-4dfb-97a7-7653d5efb83a/content/inq_chapter12_215_2.tif"/> is an equivalence of categories.
