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...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).展开更多
We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determina...We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determinant detr,sT is a quasi-central element in Fun(GLr,s(n))generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang.The explicit formulation provides an interpretation of the deforming parameters,and the quantized algebra Ur,s(R)is identified to Ur,s(gln)as the dual algebra.We then construct n−1 quasi-central elements in Ur,s(R)which are analogs of higher Casimir elements in Uq(gln).展开更多
基金supported by National Natural Science Foundation of China(Grant No.11471282)
文摘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Naihuan Jing gratefully acknowledges the support of Humboldt Foundation,MPILeipzig,Simons Foundation grant 198129and NSFC grant 11271138 during this work.Ming Liu thanks the support of NSFC grant 11271238.
文摘We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determinant detr,sT is a quasi-central element in Fun(GLr,s(n))generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang.The explicit formulation provides an interpretation of the deforming parameters,and the quantized algebra Ur,s(R)is identified to Ur,s(gln)as the dual algebra.We then construct n−1 quasi-central elements in Ur,s(R)which are analogs of higher Casimir elements in Uq(gln).
