量子群U_q(f(K,K))的弱Ore扩张及其弱Hopf代数结构

Weak Ore Extension and Structure of Weak Hopf Algebras of Quntum Groups U_q(f(K,K))

构造了一个新代数结构Uq(f(K,K)),由满足一定关系的元E,F,K,K生成的结合代数,通过对其上的结构以及基本性质的讨论证明了Uq(f(K,K))是诺特环k[K,K]的弱Ore扩张,从而证明了Uq(f(K,K))是诺特环,并且进一步在弱Hopf代数意义下给出了Uq(f(K,K))具有弱Hopf代数结构的充要条件.

An algebra Uq（f（K,K）） is constructed,it is an associative algebra generated by quadruple E,F,K, satisfying some relations.By discussing the basic properties it is proved that Uq（f（K,K）） is weak Ore extension of Noetherian ring k,so Uq（f（K,K）） is a Noetherian ring.Furthermore the necessary and sucient conditions of Uq（f（K,K）） which have a structure of weak Hopf algebra under the denotation of weak Hopf algebra is given.