Ore扩张在量子群中的应用

APPLICATIONS OF ORE EXTENSION TO QUANTUM GROUPS

证明了两类重要的量子群Ｍｑ（ｎ）及Ｕｑ（ｓｌ２）都是Ｃ上多次Ｏｒｅ扩张代数，因而都是Ｎｏｅｔｈｅｒｉａｎ．最后指出一个重要的事实：在物理上有着广泛应用的量子群Ｕｑ（ｓｌ∧２）是非Ｎｏｅｔｈｅｒｉａｎ．

It is proved that two kinds of quantum groups M q(n) and U q(sl 2) are algebras of iterated Ore extension over C, therefore they are noetherian. The last part of the paper shows an important fact that quantum groups U q( sl 2 ∧) ,which was widely applied to physics, is non noetherian.