Finite dimensional ribbon Hopf （super） algebras play an important role in constructing invariants of 3-manifolds. In the present paper, the authors give a necessary and sufficient condition for the Drinfel＇d double...Finite dimensional ribbon Hopf （super） algebras play an important role in constructing invariants of 3-manifolds. In the present paper, the authors give a necessary and sufficient condition for the Drinfel＇d double of a finite dimensional Hopf superalgebra to have a ribbon element. The criterion can be seen as a generalization of Kauffman and Radford＇s result in the non-super situation to the Z2-graded situation, however, the derivation of the result in the Z2-graded case will be much more complicated.展开更多
A new quasitriangular Hopf superalgebra and its universal R matrix for the quantum Yang-Baxter equation is constructed by endowing a simple C superalgebra generated by two even elements, one odd element and a unit wit...A new quasitriangular Hopf superalgebra and its universal R matrix for the quantum Yang-Baxter equation is constructed by endowing a simple C superalgebra generated by two even elements, one odd element and a unit with a. noncocommutative Hopf superalgebra structure.展开更多
A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b...A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b（ik）, c（ik）, g（ik）, h（ik）（i ∈I, k = 1,..., mi） of a Hopf algebra H to the quantized enveloping algebra Uq（G） of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =（aij）i,j∈I. Therefore, we define an extended Hopf superalgebra HUq（G）. We also discuss the basis and the grouplike elements of HUqG.展开更多
Finite dimensional Hopf superalgebras Uq （sl（m│n）） corresponding to the Lie superalgebras s[（m│n） are constructed. The PBW type basis and the left and right integrals of uq（sl（m│n）） are obtained. Furtherm...Finite dimensional Hopf superalgebras Uq （sl（m│n）） corresponding to the Lie superalgebras s[（m│n） are constructed. The PBW type basis and the left and right integrals of uq（sl（m│n）） are obtained. Furthermore, the group of Hopf superalgebra automorphisms is described.展开更多
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
In this paper,a super version of the Hopf quiver theory is developed.The notion of Hopf superquivers is introduced.It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra str...In this paper,a super version of the Hopf quiver theory is developed.The notion of Hopf superquivers is introduced.It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures.A complete classification of such graded Hopf superalgebras is given.A superquiver setting for general pointed Hopf superalgebras is also built up.In particular,a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11701019,11671024)the Natural Science Foundation of Beijing(No.1162002)
文摘Finite dimensional ribbon Hopf （super） algebras play an important role in constructing invariants of 3-manifolds. In the present paper, the authors give a necessary and sufficient condition for the Drinfel＇d double of a finite dimensional Hopf superalgebra to have a ribbon element. The criterion can be seen as a generalization of Kauffman and Radford＇s result in the non-super situation to the Z2-graded situation, however, the derivation of the result in the Z2-graded case will be much more complicated.
文摘A new quasitriangular Hopf superalgebra and its universal R matrix for the quantum Yang-Baxter equation is constructed by endowing a simple C superalgebra generated by two even elements, one odd element and a unit with a. noncocommutative Hopf superalgebra structure.
基金Supported by National Natural Science Foundation of China(Grant No.11171296)the Foundation of Zhejiang Provincial Educational Committee(Grant Nos.Y201327644 and FX2014082)the Natural Science Foundation of Zhejiang Province(Grant Nos.Q13A01005 and LZ14A010001)
文摘A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b（ik）, c（ik）, g（ik）, h（ik）（i ∈I, k = 1,..., mi） of a Hopf algebra H to the quantized enveloping algebra Uq（G） of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =（aij）i,j∈I. Therefore, we define an extended Hopf superalgebra HUq（G）. We also discuss the basis and the grouplike elements of HUqG.
文摘Finite dimensional Hopf superalgebras Uq （sl（m│n）） corresponding to the Lie superalgebras s[（m│n） are constructed. The PBW type basis and the left and right integrals of uq（sl（m│n）） are obtained. Furthermore, the group of Hopf superalgebra automorphisms is described.
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
基金Project supported by the National Natural Science Foundation of China (No. 10601052)the Shandong Provincial Natural Science Foundation of China (Nos. YZ2008A05, 2009ZRA01128)
文摘In this paper,a super version of the Hopf quiver theory is developed.The notion of Hopf superquivers is introduced.It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures.A complete classification of such graded Hopf superalgebras is given.A superquiver setting for general pointed Hopf superalgebras is also built up.In particular,a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given.
基金supported by NSFC(No.11171296)the Foundation of Zhejiang Provincial Educational Committee(No.Y201327644,No.FX2014082)the Natural Science Foundation of Zhejiang Province(No.LQ13A010018,No.LZ14A010001,No.LY15A010002)
