Abstract:

We first introduced the notions of partial DoiHopf group structures and partial DoiHopf group modules which generalize Doi-Hopf structures and DoiHopf modules. Then we gave some examples and basic properties. Mainly we combined the idea of group coalgebras with partial entwining structures to construct the forgetful functor from the category of partial DoiHopf group modules to that of modules and proved that it has a right adjoint functor.

Key words: partial DoiHopf group structure, partial DoiHopf  group module, forgetful functor