Let π be a group with a unit 1; H is a Hopf π- coalgebra and A is a right π-H-comodule algebra. First, the notion of a two-sided relative （A, H）-Hopf π-comodule is introduced; then it is obtained that Hom A H （...Let π be a group with a unit 1; H is a Hopf π- coalgebra and A is a right π-H-comodule algebra. First, the notion of a two-sided relative （A, H）-Hopf π-comodule is introduced; then it is obtained that Hom A H （M, N） H and HOMA（M, N） are isomorphic as right Hopf π-H-comodules, where Hom A H（M, N） denotes the space of right A-module fight H-comodule morphisms and HOMa （M, N） denotes the rational space of a space Hom A（M, N） of right A-module morphisms. Secondly, the structure theorem of endomorphism algebras of two-sided relative （A, H）-Hopf π--comodules is established; that is, End A H （M）#H and END A（M, N） are isomorphic as fight Hopf π-H-comodules and algebras.展开更多
Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of ...Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.展开更多
A large class of algebras(possibly nonassociative)with group-coalgebraic structures,called quasigroup Hopf group-coalgebras,is introduced and studied.Quasigroup Hopf group-coalgebras provide a unifying framework for t...A large class of algebras(possibly nonassociative)with group-coalgebraic structures,called quasigroup Hopf group-coalgebras,is introduced and studied.Quasigroup Hopf group-coalgebras provide a unifying framework for the classical Hopf algebras and Hopf group-coalgebras as well as Hopf quasigroups.Then,basic results similar to those in Hopf algebras H are proved,such as anti-(co)multiplicativity of the antipode S:H→H,and S^(2)=id if H is commutative or cocommutative.展开更多
基金The Research and Innovation Project for College Graduates of Jiangsu Province(No.CXLX_0094)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘Let π be a group with a unit 1; H is a Hopf π- coalgebra and A is a right π-H-comodule algebra. First, the notion of a two-sided relative （A, H）-Hopf π-comodule is introduced; then it is obtained that Hom A H （M, N） H and HOMA（M, N） are isomorphic as right Hopf π-H-comodules, where Hom A H（M, N） denotes the space of right A-module fight H-comodule morphisms and HOMa （M, N） denotes the rational space of a space Hom A（M, N） of right A-module morphisms. Secondly, the structure theorem of endomorphism algebras of two-sided relative （A, H）-Hopf π--comodules is established; that is, End A H （M）#H and END A（M, N） are isomorphic as fight Hopf π-H-comodules and algebras.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)the Fundamental Research Funds for the Central Universities(No.KYZZ0060)
文摘Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)the Natural Science Foundation of Jiangsu Province(No.BK20171348).
文摘A large class of algebras(possibly nonassociative)with group-coalgebraic structures,called quasigroup Hopf group-coalgebras,is introduced and studied.Quasigroup Hopf group-coalgebras provide a unifying framework for the classical Hopf algebras and Hopf group-coalgebras as well as Hopf quasigroups.Then,basic results similar to those in Hopf algebras H are proved,such as anti-(co)multiplicativity of the antipode S:H→H,and S^(2)=id if H is commutative or cocommutative.
