Let , be two partial Doi-Hopf datums consisting of a Hopf algebra , a partial right -comodule algebra and a partial right -module coalgebra. Given , and , we define an induction functor between the category of all partial Doi-Hopf modules and the category , and we prove that this functor has a right adjoint. Specially, we then give necessary and sufficient conditions for the functor (exactly the category of right -modules). This leads to a generalized notion of integrals. Moreover, from these results, we deduce a version of Maschke-type Theorems for partial Doi-Hopf modules. The applications of our results are considered.
Cite this article
Q.-C. Chen, D.-G. Wang, The Category of Partial Doi-Hopf Modules and Functors. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 189–204DOI 10.4171/RSMUP/129-11