摘要
Let A be a subalgebra of uq（sl（2）） generated by K, K-1 and F and A^δ be a subalgebra of b/q（sl（2）） generated by K, K-1 （and also Fd if q is a primitive d-th root of unity with d an odd number）. Given an Aδ-module M, a/gq（s/（2））-module A A M is constructed via the iterated Ore extension of Uq（S/（2）） in a unified framework for any q. Then all the submodules of A δA5 M are determined for a fixed finite-dimensional indecomposable Aδ-module .M. It turns out that for some indecomposable A^-module M, the 5/q（sl（2））-module A @A M is indecomposable, which is not in the BGG-categories associated with quantum groups in general.
Let A be a subalgebra of uq（sl（2）） generated by K, K-1 and F and A^δ be a subalgebra of b/q（sl（2）） generated by K, K-1 （and also Fd if q is a primitive d-th root of unity with d an odd number）. Given an Aδ-module M, a/gq（s/（2））-module A A M is constructed via the iterated Ore extension of Uq（S/（2）） in a unified framework for any q. Then all the submodules of A δA5 M are determined for a fixed finite-dimensional indecomposable Aδ-module .M. It turns out that for some indecomposable A^-module M, the 5/q（sl（2））-module A @A M is indecomposable, which is not in the BGG-categories associated with quantum groups in general.
基金
Supported by National Natural Foundation of China (Grant No. 11171291)
Doctorate Foundation (Grant No. 200811170001) Ministry of Education of China
