摘要
Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).
Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q（g,Λ）and U= U_q（g,Q）be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q（g,Λ）, which corresponds to the Casimir element of the enveloping algebra U（g）. Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q（g,Λ） and U = U_q（g,Q）.
基金
supported by National Natural Science Foundation of China(Grant No.11471282)
