In this paper, author studies the rigidity of quasi-Casimir elements, and associate them with root-systems. Moreover, Yang-Baxter operators are constructed as compositions of quasi-Casimir elements and quasi-transposi...In this paper, author studies the rigidity of quasi-Casimir elements, and associate them with root-systems. Moreover, Yang-Baxter operators are constructed as compositions of quasi-Casimir elements and quasi-transpositions.展开更多
The author constructs the Casimir element of Hall algebras. By the method of Gabber-Kac theorem (see [4]), it is proved that the Serre relations are the defining relations in composition algebra.
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
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 construct a new quantum group Uq（osp（1,2,f））,which can be seen as a generalization of Uq（osp（1,2））.A necessary and sufficient condition for the algebra Uq（osp（1,2,f）） to be a super Hopf al...In this paper we construct a new quantum group Uq（osp（1,2,f））,which can be seen as a generalization of Uq（osp（1,2））.A necessary and sufficient condition for the algebra Uq（osp（1,2,f）） to be a super Hopf algebra is obtained and the center Z（Uq（osp（1,2,f））） is given.展开更多
文摘In this paper, author studies the rigidity of quasi-Casimir elements, and associate them with root-systems. Moreover, Yang-Baxter operators are constructed as compositions of quasi-Casimir elements and quasi-transpositions.
文摘The author constructs the Casimir element of Hall algebras. By the method of Gabber-Kac theorem (see [4]), it is proved that the Serre relations are the defining relations in composition algebra.
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).
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 the National Natural Science Foundation of China (Grant Nos.10971049 10971052) +1 种基金the Natural Science Foundation of Hebei Province (Grant Nos.A2008000135 A2009000253)
文摘In this paper we construct a new quantum group Uq（osp（1,2,f））,which can be seen as a generalization of Uq（osp（1,2））.A necessary and sufficient condition for the algebra Uq（osp（1,2,f）） to be a super Hopf algebra is obtained and the center Z（Uq（osp（1,2,f））） is given.
