The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The ...The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F（Uq（f（K, H））） is given.展开更多
Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finitedimensional indecomposable H-module is generated by one ele...Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finitedimensional indecomposable H-module is generated by one element.In particular,any indecomposable submodule of H under the adjoint action is generated by a special element of H.Using this result,we show that the Hopf algebra H is a principal ideal ring,i.e.,any two-sided ideal of H is generated by one element.As an application,we give explicitly the generators of ideals,primitive ideals,maximal ideals and completely prime ideals of the Taft algebras.展开更多
基金Foundation item： the National Natural Science Foundation of China （No. 10871227） the Science Foundation of Hebei Province （No. 2008000135）.
文摘The aim of this paper is to study the adjoint action for the quantum algebra Uq（f（K, H））, which is a natural generalization of quantum algebra Uq（sl2） and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F（Uq（f（K, H））） is given.
基金supported by the National Natural Science Foundation of China(Grant No.11871063)supported by the Qing Lan project.
文摘Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero.In this paper we show that any finitedimensional indecomposable H-module is generated by one element.In particular,any indecomposable submodule of H under the adjoint action is generated by a special element of H.Using this result,we show that the Hopf algebra H is a principal ideal ring,i.e.,any two-sided ideal of H is generated by one element.As an application,we give explicitly the generators of ideals,primitive ideals,maximal ideals and completely prime ideals of the Taft algebras.
