The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U...The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U_(r,s)(F_(4))is pointed,and of a Drinfel’d double structure under a certain condition.All of Hopf isomorphisms of u_(r,s)(F_(4))are determined,and the necessary and sufficient condition for u_(r,s)(F_(4))to be a ribbon Hopf algebra is singled out by describing the left and right integrals.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
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
基金Nai Hong Hu is supported by the NNSF of China(Grant Nos.12171155,12071094)in part by Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。
文摘The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U_(r,s)(F_(4))is pointed,and of a Drinfel’d double structure under a certain condition.All of Hopf isomorphisms of u_(r,s)(F_(4))are determined,and the necessary and sufficient condition for u_(r,s)(F_(4))to be a ribbon Hopf algebra is singled out by describing the left and right integrals.
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.
