Читать книгу Algebra and Applications 2 - Группа авторов - Страница 18

We introduce the crucial property of connectedness for bialgebras. The main interest resides in the possibility of implementing recursive procedures in connected bialgebras, the induction taking place with respect to a filtration or a grading. An important example of these techniques is the recursive construction of the antipode, which then “comes for free”, showing that any connected bialgebra is in fact a connected Hopf algebra.