q为偶数次本原单位根时量子群U_q(m,n)的分解

Decomposition of U_q(m,n) When q is a (2r )th Root of Unity

研究了当q为偶数次本原单位根时 ,量子群Uq(sl2 )在关系K2r=1,Emr=0 ,Fmr=0下的商代数Uq(m ,n)的构造 ,给出Uq(m ,n)的Hopf代数结构和分次代数结构 ,给出了Uq(m ,n)的所有不同构的Verma模 ,给出了Uq(m ,n)的精确到基的理想结构。把Uq(m ,n)

The restricted quantum group U q(m,n) is the quantum group U q(sl 2) with relations K r=1, E mr =0, F nr =0. If q is a ( 2r )th root of unity, the structure of U q(m,n) is different from the odd case. Hopf algebra structure and graded algebra structure of U q(m,n) is similar to the odd case,while the ideal structure is quite different. The algebra U q(m,n) is decomposed into a direct sum of principal indecomposable modules.