Quantum Adjoint Action for Quantum Algebra ${\cal U}_q(f(K,H))$
Received:December 25, 2006  Revised:November 22, 2007
Key Word: adjoint action   locally finite subalgebra   highest weight vector.  
Fund ProjectL:the National Natural Science Foundation of China (No.10871227); the Science Foundation of Hebei Province (No.2008000135).
Author NameAffiliation
HOU Bo College of Mathematics and Information Science, Hebei Teacher's University, Hebei 050016, China 
WANG Zhi Xi Department of Mathematics, Capital Normal University, Beijing 100037, China 
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      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.
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