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,we investigate the presentation for little q-Schur algebra u_(k)(3.5)at odd roots.The Poincaré-Birkhoff-Witt(PBW)basis of u_(k)(3.5)is obtained through the basis of q-Schur algebra U(3.5).Then we pr...In this paper,we investigate the presentation for little q-Schur algebra u_(k)(3.5)at odd roots.The Poincaré-Birkhoff-Witt(PBW)basis of u_(k)(3.5)is obtained through the basis of q-Schur algebra U(3.5).Then we present a new set for generators and relations for u_(k)(3.5)by PBW basis.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Supported by the Natural Research Project of Yichang(A23-2-026)。
文摘In this paper,we investigate the presentation for little q-Schur algebra u_(k)(3.5)at odd roots.The Poincaré-Birkhoff-Witt(PBW)basis of u_(k)(3.5)is obtained through the basis of q-Schur algebra U(3.5).Then we present a new set for generators and relations for u_(k)(3.5)by PBW basis.
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.
