It is shown that the dual bialgebra of any quasitriangular bialgebra is braided, and the dual bialgebra of some braided bialgebra is quasitriangular.Also it is proved that every nondegenerate finite dimensional braid...It is shown that the dual bialgebra of any quasitriangular bialgebra is braided, and the dual bialgebra of some braided bialgebra is quasitriangular.Also it is proved that every nondegenerate finite dimensional braided (dually, quasitriangular) bialgebra has an antipode.展开更多
Let A be a bialgebra, R ∈ A A be a strong “cocycle”. It will be shown that the monoidal category _Auhas a braided monoidal subcategory and several equivalent conditions for (A, R ) to be a quasitriangular bialgebra...Let A be a bialgebra, R ∈ A A be a strong “cocycle”. It will be shown that the monoidal category _Auhas a braided monoidal subcategory and several equivalent conditions for (A, R ) to be a quasitriangular bialgebra will be given. Furthermore, it will be shown that A contains a finite dimensional subbialgebra which is a quasitriangular Hopf algebra if R is a YB-operator.展开更多
文摘It is shown that the dual bialgebra of any quasitriangular bialgebra is braided, and the dual bialgebra of some braided bialgebra is quasitriangular.Also it is proved that every nondegenerate finite dimensional braided (dually, quasitriangular) bialgebra has an antipode.
文摘Let A be a bialgebra, R ∈ A A be a strong “cocycle”. It will be shown that the monoidal category _Auhas a braided monoidal subcategory and several equivalent conditions for (A, R ) to be a quasitriangular bialgebra will be given. Furthermore, it will be shown that A contains a finite dimensional subbialgebra which is a quasitriangular Hopf algebra if R is a YB-operator.
