-catégories (catégories dans un triple)
Quantum integrals associated to quantum Hom-Yetter-Drinfel’d modules are defined, and the affineness criterion for quantum Hom-Yetter-Drinfel’d modules is proved in the following form. Let (H,α) be a monoidal Hom-Hopf algebra, (A,β) an (H,α)-Hom-bicomodule algebra and . Under the assumption that there exists a total quantum integral γ: H → Hom(H,A) and the canonical map , , is surjective, we prove that the induction functor is an equivalence of categories.
We determine the algebraic groups which have a close relation to the Roth inequalities.