Classification of Infinitely Dimensional Indecomposable U_q（sl₂）-modules

In this paper , we first give indecomposable Harish - Chandra Uq ( sl2 ) - Classification of the mold , and then discuss the tensor product standard grumble Uq ( sl2 ) mode . Finite-dimensional simple Lie algebra g quantum deformation Uq ( g ) ( moving either in mathematics or in the physical aspects occupy a very important position , especially in the Yang-Baxter equation , two-dimensional solvable lattice analog and analog aspects has been widely used in Drinfeld - Jimbo quantum group in quantum enveloping algebra Uq ( sl2 ) is the most important and simple example . study algebra Uq ( sl2 ) Indicates critical when q is not a unit root UQ ( g ) of the representation theory of finite dimensional and U ( g ) is similar to the theory , that is to say , UQ ( g ) U ( g ) that the q- deformation However , classification infinite-dimensional indecomposable Uq ( g ) mode and few people pay attention to the purpose of this thesis is to reconcile analytics algebra grumble Uq ( sl2 ) classification method is extended to a single representation of the Lie algebra sl ( 2 ) algebra UQ ( SL2 ) 2 construct infinite-dimensional indecomposable representation of Uq ( sl2 ) .