In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is...In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is called the Hom-dimodule is introduced and its properties are discussed Moreover the category of Hom-dimodules in connection with the Hom D-equation R12 R23 =R23 R12 for R∈Endk M⊙M and a Hom-module M is investigated.Some solutions of the Hom D-equation from Hom-dimodules over Hom-bialgebras are given and the FRT-type theorem is constructed in the category of Hom-dimodules. The results generalize and improve the FRT-type theorem in the category of dimodules.展开更多
基金The National Natural Science Foundation of China(No.11371089)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Postdoctoral Innovation Funds of Southeast University(No.3207013601)
文摘In order to study the deformation of algebras the notions of Hom-algebras are introduced.The Hom-algebra is a generalization of the classical associative algebra.First the Hom-type generalization of dimodules which is called the Hom-dimodule is introduced and its properties are discussed Moreover the category of Hom-dimodules in connection with the Hom D-equation R12 R23 =R23 R12 for R∈Endk M⊙M and a Hom-module M is investigated.Some solutions of the Hom D-equation from Hom-dimodules over Hom-bialgebras are given and the FRT-type theorem is constructed in the category of Hom-dimodules. The results generalize and improve the FRT-type theorem in the category of dimodules.
