A class of two-parameter quantum algebras Ur,s（s[（m｜n）） is constructed. It is shown that Ur,s（s[（m｜n）） is a Hopf superalgebra. Then the PBW basis of Ur,s（s[（m｜n）） is described. For this purpose, some co...A class of two-parameter quantum algebras Ur,s（s[（m｜n）） is constructed. It is shown that Ur,s（s[（m｜n）） is a Hopf superalgebra. Then the PBW basis of Ur,s（s[（m｜n）） is described. For this purpose, some commutative relations of root vectors of U^＋r,s（s[（m｜n）） are given展开更多
Recently the quantum toroidal superalgebraε_(m|n)associated with gl_(m|n)was introduced by L.Bezerra and E.Mukhin,which is not a quantum Kac-Moody algebra.The quantum toroidal superalgebraε_(m|n)exploits infinite se...Recently the quantum toroidal superalgebraε_(m|n)associated with gl_(m|n)was introduced by L.Bezerra and E.Mukhin,which is not a quantum Kac-Moody algebra.The quantum toroidal superalgebraε_(m|n)exploits infinite sequences of generators and relations of the form,which are called Drinfeld realization.In this paper,we use only finite set of generators and relations to define an associative algebraε'_(m|n)and show that there exists an epimorphism fromε'_(m|n)to the quantum toroidal superalgebraε_(m|n).In particular,the structure ofε'_(m|n)enjoys some properties like Drinfeld-Jimbo realization.展开更多
By the R-matrix of orthosymplectic quantum superalgebra Uq （osp（2l＋ 1｜2n）） in the vector representation, we establish the corresponding quantum Hopf superalgebra OSPq（2l＋ 1｜2n）. Furthermore, it is shown that...By the R-matrix of orthosymplectic quantum superalgebra Uq （osp（2l＋ 1｜2n）） in the vector representation, we establish the corresponding quantum Hopf superalgebra OSPq（2l＋ 1｜2n）. Furthermore, it is shown that OSPq（2l＋ 1｜2n） is coquasitriangular. Keywords R-matrix, super bialgebra, quantum function superalgebras展开更多
We construct fermionic-bosonic representations for a class of generalized B（m, n）, C（n）, D（m, n）-graded Lie superalgebras coordinatized by quantum tori with nontrivial central extensions.
In this paper, we embed the integral form of the quantum supergroup U_v(gl_(m|n)) to the product of a family of integral quantum Schur super algebras. We show that the image of the embedding is a free Z[v, v^(-1)]-mod...In this paper, we embed the integral form of the quantum supergroup U_v(gl_(m|n)) to the product of a family of integral quantum Schur super algebras. We show that the image of the embedding is a free Z[v, v^(-1)]-module by finding the basis explicitly and calculating the fundamental multiplication formulas of these bases. Unlike the non-super case, the fundamental multiplication formula, which is the key step, is more complicated since we have to deal with the case of multiplying the odd root vectors. As a consequence, via the base change, we realize the quantum supergroup at roots of unity as a subalgebra of the product of quantum Schur superalgebras. Thus, we find a new basis of quantum supergroups at odd roots of unity which comes from quantum Schur superalgebras.展开更多
基金The second author was supported by Beijing Natural Science Foundation （Grant No. 1122006）, the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20111103110011） and partially supported by the National Natural Science Foundation of China （Grant No. 11271043, 11471186）.
文摘A class of two-parameter quantum algebras Ur,s（s[（m｜n）） is constructed. It is shown that Ur,s（s[（m｜n）） is a Hopf superalgebra. Then the PBW basis of Ur,s（s[（m｜n）） is described. For this purpose, some commutative relations of root vectors of U^＋r,s（s[（m｜n）） are given
文摘Recently the quantum toroidal superalgebraε_(m|n)associated with gl_(m|n)was introduced by L.Bezerra and E.Mukhin,which is not a quantum Kac-Moody algebra.The quantum toroidal superalgebraε_(m|n)exploits infinite sequences of generators and relations of the form,which are called Drinfeld realization.In this paper,we use only finite set of generators and relations to define an associative algebraε'_(m|n)and show that there exists an epimorphism fromε'_(m|n)to the quantum toroidal superalgebraε_(m|n).In particular,the structure ofε'_(m|n)enjoys some properties like Drinfeld-Jimbo realization.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10671016, 10771014） and Foundation of Selected Excellent Science and Technology Activity for Returned Scholars of Beijing
文摘By the R-matrix of orthosymplectic quantum superalgebra Uq （osp（2l＋ 1｜2n）） in the vector representation, we establish the corresponding quantum Hopf superalgebra OSPq（2l＋ 1｜2n）. Furthermore, it is shown that OSPq（2l＋ 1｜2n） is coquasitriangular. Keywords R-matrix, super bialgebra, quantum function superalgebras
文摘We construct fermionic-bosonic representations for a class of generalized B（m, n）, C（n）, D（m, n）-graded Lie superalgebras coordinatized by quantum tori with nontrivial central extensions.
基金supported by National Natural Science Foundation of China (Grant No. 11501546)K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we embed the integral form of the quantum supergroup U_v(gl_(m|n)) to the product of a family of integral quantum Schur super algebras. We show that the image of the embedding is a free Z[v, v^(-1)]-module by finding the basis explicitly and calculating the fundamental multiplication formulas of these bases. Unlike the non-super case, the fundamental multiplication formula, which is the key step, is more complicated since we have to deal with the case of multiplying the odd root vectors. As a consequence, via the base change, we realize the quantum supergroup at roots of unity as a subalgebra of the product of quantum Schur superalgebras. Thus, we find a new basis of quantum supergroups at odd roots of unity which comes from quantum Schur superalgebras.
