On the indecomposable modules of U q (sl(2)) constructed via ore-extension

Let A be a subalgebra of U q (sl(2)) generated by K,K .1 and F and A . be a subalgebra of U q (sl(2)) generated by K,K .1 (and also F d if q is a primitive d-th root of unity with d an odd number). Given an A .-module M, a U q (sl(2))-module A.A.M is constructed via the iterated Ore extension of U q (sl(2)) in a unified framework for any q. Then all the submodules of A.A.M are determined for a fixed finite-dimensional indecomposable A .-module M. It turns out that for some indecomposable A .-module M, the U q (sl(2))-module A.A.M is indecomposable, which is not in the BGG-categories O q associated with quantum groups in general.