The Irreducible Representation And The Center Of The Quantum Algebra U_q(f(K))

Quantum groups theory is one of the important branches of algebraic areas, and has been widely studied from the middle of the eighties in the last century. The aim of this thesis is to study the center and the simple representations of quantum algebra Ug(f(K)) in the case q is a primitive e-th root of unity with lIn the first part we indicate three kinds to discuss the irreducible representations of quantum algebra Uq(f(K)), when q is a primitive root of unity. In the second part, we prove that the center of Uq(f(K)) is generated by El,Fl, Kl, K-l, Cq.