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
In this paper,we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups.Our methods depend on the theory of braided strict monoidal categ...In this paper,we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups.Our methods depend on the theory of braided strict monoidal categories which are pivotal,more explicitly,the diagram category of framed tangles.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supported by National Natural Science Foundation of China(Grant No.11301195)China Scholarship Council and a research foundation of Huaqiao University(Grant No.2014KJTD14)。
文摘In this paper,we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups.Our methods depend on the theory of braided strict monoidal categories which are pivotal,more explicitly,the diagram category of framed tangles.
