关键词: 量子Loop代数, 权模, 单模, Dense模

Abstract: The structural problem of simple weight modules with a one-dimensional weight space in the quantum Loop algebra U_q(L(sl₂)) was solved by using a construction method, and it was obtained that any simple weight module with a one-dimensional weight space must be  isomorphic to one of the four classes of simple weight modules of U_q(L(sl₂)). In addition, a class of simple weight modules of  the quantum Loop algebra U_q(L(sl₂)) with  weight space dimension of 2, which was neither the highest weight nor the lowest weight, was constructed.

Key words: quantum Loop algebra, weight module, simple module, Dense module