量子代数${\cal U}_q(f(K,H))$的量子伴随作用

Quantum Adjoint Action for Quantum Algebra ${\cal U}_q(f(K,H))$

中文关键词:  伴随作用  局部有限子代数  最高权向量.

英文关键词:adjoint action  locally finite subalgebra  highest weight vector.

中文摘要:

      量子代数${\cal U}_q(f(K,H))$是量子代数${\cal U}_q(sl_2)$的一种自然推广形式,并且可以认为是一类广义Weyl代数.本文主要研究其上的量子伴随作用,给出了在此作用下其局部有限子代数${\cal F}({\cal U}_q(f(K,H)))$的结构定理.

英文摘要:

      The aim of this paper is to study the adjoint action for the quantum algebra ${\cal U}_q(f(K,H))$, which is a natural generalization of quantum algebra ${\cal U}_q({\rm sl}_2)$ and is regarded as a class of generalized Weyl algebra. The structure theorem of its locally finite subalgebra ${\cal F}({\cal U}_q(f(K,H)))$ is given.