Coideal subalgebras of pointed and connected Hopf algebras (Q6567148)

It is proved that if \(B\subset A\) are two left- or right-coideal subalgebras of a pointed Hopf algebra \(H\) that contain the coradical of \(H\), if this coradical is abelian and with other technical conditions, then \(A\) has a Poincaré-Birkhoff-Witt basis overs \(B\). Here \(H\) is connected and graded and over a field of characteristic zero, and if \(A\) and \(B\) are both homogeneous and of finite Gelfand-Kirillov dimension, then \(A\) is an iterated Ore extension of \(B\). Both these results are consequences of a more general theorem on pairs of homogeneous graded coideal subalgebras of a connected and graded braided Hopf algebra, presented and proved in this paper.